Huoxiong Wu

Xiamen University | XMU · School of Mathematical Sciences

In this paper, we study the behaviours of the commutators $[\vec b,\,T]$ generated by multilinear Calderón–Zygmund operators $T$ with $\vec b=(b_1,\,\ldots,\,b_m)\in L_{\rm loc}(\mathbb {R}^n)$ on weighted Hardy spaces. We show that for some $p_i\in (0,\,1]$ with $1/p=1/p_1+\cdots +1/p_m$ , $\omega \in A_\infty$ and $b_i\in \mathcal {BMO}_{\omega,p...

In this paper, the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces, which essentially extend and improve the previous known results obtained by Grafakos and Kalton (2001) and Li, Xue and Yabuta (2011). The corresponding...

This paper gives pointwise sparse domination results for variation operators of singular integrals and commutators with kernels satisfying \(L^r\)-Hörmander conditions. As applications, we obtain strong-type quantitative weighted bounds for such variation operators, weak-type quantitative weighted bounds for the variation operators of singular inte...

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

This paper gives new two-weight bump conditions for the sparse operators related to iterated commutators of fractional integrals. As applications, the two-weight bounds for iterated commutators of fractional integrals under more general bump conditions are obtained. Meanwhile, the necessity of two-weight bump conditions as well as the converse of B...

This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H\"{o}rmander conditions. As applications, we obtain the strong type quantitative weighted bounds for such variation operators as well as the weak-type quantitative weighted bounds for the variation opera...

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new CMO(Rn) characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

This paper explores the limiting weak-type behaviors of certain classical operators in harmonic analysis including maximal operators, singular and fractional integral operators and maximal truncated singular integrals as well as the general convolution operators with weak-type Young’s inequalities. Some optimal limiting weak-type behaviors are give...

Let λ∈(−12,∞) and Sλ≔−d2dx2+λ2−λx2 be the Bessel Schrödinger operator on R+≔(0,∞). The authors obtain the sharp power-weighted Lp, weak type and restricted weak type inequalities for the oscillation operator O{ti}i∈N({tm∂tmWtλ}t>0,⋅) and the variation operator Vρ({tm∂tmWtλ}t>0,⋅) of the heat semigroup {Wtλ}t>0 associated with Sλ, where ρ∈(2,∞) and...

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $BMO$ type spaces via the boundedness of variation operators associated with approximate identities and their commutators, respectively.

This paper studies the two-weight estimates of variation and oscillation operators for commutators of singular integrals with weighted {\mathrm{BMO}} functions. A new characterization of weighted {\mathrm{BMO}} spaces via the boundedness of variation and oscillation operators for the iterated commutators of Calderón–Zygmund singular integrals in th...

In this paper, we extend the mixed weak-type inequalities of Sawyer type for Calderon-Zygmund operators to the variation operators of θ-type Calderon-Zygmund operators. Moreover, the corresponding quantitative weighted bounds as well as the weighted estimates in the extreme case p=∞ are also obtained. Meanwhile, we also present the quantitative Blo...

In this paper, we study the commutators generated by Lipschitz functions and fractional type integral operators with kernels of the form Kα(x,y)=κ1(x−A1y)κ2(x−A2y)⋯κm(x−Amy), where 0≤α=α1+⋯+αm

This paper gives a characterization of compactness for maximal commutators with rough kernels in weighted Lebesgue spaces, which is new and interesting even in un-weighted cases. Meanwhile, a new characterization of weighted boundedness for such operators is also established.

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new $CMO(\mathbb{R}^n)$ characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

Let λ∈(0,∞) and △λ:=−d2dx2−2λxddx be the Bessel operator on ℝ+:=(0,∞). In this paper, the authors show that b∈BMO(ℝ+,dmλ) (or CMO(ℝ+,dmλ), respectively) if and only if the Riesz transform commutator [b,R△λ] is bounded (or compact, respectively) on Morrey spaces Lp,κ(ℝ+,dmλ), where dmλ(x):=x2λdx, p∈(1,∞) and κ∈(0,1). A weak factorization theorem for...

Let [Formula: see text], [Formula: see text] and [Formula: see text] be a singular or fractional integral operator with homogeneous kernel [Formula: see text]. In this paper, a CMO type space [Formula: see text] is introduced and studied. In particular, the relationship between [Formula: see text] and the Lipchitz space [Formula: see text] is discu...

A new characterization of CMO(R^n) is established by the local mean oscillation. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.

In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type behaviors are given, which essentially improve and extend the previous results in this topics.

This paper gives unified criterions on the necessity of bounded commutators in linear and multilinear settings. Our results relax the restriction of Banach spaces in previous results to quasi-Banach spaces and extend \(BMO(\mathbb {R}^n)\) to the general \(BMO_\mu \), which includes \(BMO(\mathbb {R}^n)\), \(\mathrm{Lip}_\beta (\mathbb {R}^n)\), an...

We prove that the maximal operators supported by submanifolds are bounded and continuous on the Triebel-Lizorkin spaces and Besov spaces for and . As a corollary, we also show that these operators are bounded and continuous on the fractional Sobolev spaces for and . Our main results represent significant improvements as well as natural extensions o...

In this paper, we investigate the integrability and asymptotic behaviors of positive solutions for a nonlinear integral system in a functional setting. Using the regularity lifting lemma and some delicate analysis techniques, we obtain the optimal integral intervals and the asymptotic estimates for such solutions around the origin and near infinity...

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also consider the inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spaces $W_{p,q}^s$, which essentially improve and extend the main results obtained by Cunanana, Kobayashib and...

In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for $p\leq 1$, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (...

In this paper, we study some important properties of positive solutions for a nonlinear integral system. With the help of the method of moving planes in an integral form, we show that under certain integrable conditions, all of positive solutions to this system are radially symmetric and decreasing with respect to the origin. Meanwhile, using the r...

In this note we give a simple proof of the endpoint regularity for the uncentred Hardy–Littlewood maximal function on $\mathbb{R}$ . Our proof is based on identities for the local maximum points of the corresponding maximal functions, which are of interest in their own right.

In this paper, we consider the embedding relations between any two $\alpha$% -modulation spaces. Based on an observation that the $\alpha$-modulation space with smaller $\alpha$ can be regarded as a corresponding $\alpha$% -modulation space with larger $\alpha$, we give a complete characterization of the Fourier multipliers between $\alpha$-modulat...

Let $\lambda>0$ and $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator on $\mathbb R_+:=(0,\infty)$. We show that the oscillation operator ${\mathcal O(P^{[\lambda]}_\ast)}$ and variation operator ${\mathcal V}_\rho(P^{[\lambda]}_\ast)$ of the Poisson semigroup $\{P^{[\lambda]}_t\}_{t>0}$ associated with $\...

Let λ > 0 and let be the Bessel operator on ℝ + := (0, ∞ ). We show that the oscillation operator 𝒪 ( R Δ λ , ∗ ) and variation operator 𝒱 ρ ( R Δ λ , ∗ ) of the Riesz transform R Δ λ associated with Δ λ are both bounded on L p (ℝ + , d m λ ) for p ∈ (1, ∞ ), from L¹ (ℝ + , d m λ ) to L 1 ,∞ (ℝ + , d m λ ), and from L ∞ (ℝ + , d m λ ) to BMO(ℝ + ,...

Let $\lambda>0$ and $\triangle_\lambda:=-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be the Bessel operator on $\mathbb R_+:=(0,\infty)$. We first introduce and obtain an equivalent characterization of ${\rm CMO}(\mathbb R_+,\, x^{2\lambda}dx)$. By this equivalent characterization and establishing a new version of the Fr\'{e}chet-Kolmogorov th...

In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, we also obtain the weakest conditions for the boundedness of bilinear Fourier multipliers on modulation s...

In this paper, we consider the singular integrals related to homogeneous mappings as well as the corresponding maximal truncated singular integrals. Under the rather weak size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds for such operators are given, which essentially improve and generalize s...

Let b ∈ BMO(Rn) and MΩ be the Marcinkiewicz integral operator with kernel (Formula Presented), where Ω is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn−1. In this paper, by means of Fourier transform estimates and approximation to the operator MΩ with integral operators having smooth kernels we show that if b...

This paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-...

In this paper, we give a criterion of boundedness for the operators of convolution type on Triebel-Lizorkin spaces. As applications, under rather weak size conditions, the bounds for the singular integrals along certain compound surfaces on the above function spaces are obtained. Some previous results are improved and extended.

This paper gives a T(b) type theorem, which is a boundedness criterion for singular integral operators from the weighted Herz-type Hardy spaces into the weighted local Herz-type Hardy spaces. As applications, the corresponding mapping properties for the Cauchy integral and Calderón's commutators are obtained. In addition, a counter example is shown...

We obtain some optimal properties on weighted modulation spaces. We find the necessary and sufficient conditions for product inequalities, convolution inequalities and embedding on weighted modulation spaces. Especially, we establish the analogue of the sharp Sobolev embedding theorem on weighted modulation spaces. © 2015 Science China Press and Sp...

This paper is devoted to investigating the bounded behaviors of the oscillation and variation operators for Calderón-Zygmund singular integrals and the corresponding commutators on the weighted Morrey spaces. We establish several criterions of boundedness, which are applied to obtain the corresponding bounds for the oscillation and variation operat...

In this paper, we solve a long standing problem on the modulation spaces, (Formula presented.)-modulation spaces and Besov spaces. We establish sharp conditions for the complex interpolation between these function spaces. We show that no (Formula presented.)-modulation space (Formula presented.) can be regarded as the interpolation space between (F...

This paper is devoted to investigating the boundedness of the oscillation and variation operators for the commutators generated by Calderón-Zygmund singular integrals with Lipschitz functions in the weighted Lebesgue spaces and the endpoint spaces in dimension 1. Certain criterions of boundedness are given. As applications, the weighted ( L p , L q...

In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized g-function, Lusin area function and gλ∗-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from BMO(ℝn) to BLO(ℝn), which improve and generalize...

In this paper we consider the parametric Marcinkiewicz integrals with mixed homogeneity along certain compound surfaces. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp boundedness for such operators are given. As applications, the corresponding results for parametric Mar...

This paper gives a criterion on the weighted norm estimates of the oscillatory and variation operators for the commutators of Calderón-Zygmund singular integrals in dimension 1. As applications, the weighted Lp-boundedness of the oscillation operators and the ρ-variation operators for commutators of the Hilbert transform and the Hermitian Riesz tra...

Let L be a one-to-one operator of type ω having a bounded H∞, functional calculus and satisfying the k-Davies-Gaffney estimates with k ∈ N. In this article, the authors introduce the weak Hardy space WHpL(Rn) associated to L for p ∈ (0, 1] via the non-tangential square function SL and establish a weak molecular characterization of WHpL(Rn). A typic...

This paper is devoted to investigating the properties of multilinear A((P) over right arrow) conditions and A(((P) over right arrow),(q)) conditions, which are suitable for the study of multilinear operators on Lebesgue spaces; Some monotonicity properties of A((P) over right arrow) and A(((P) over right arrow ,q)) classes with respect to (P) over...

The parabolic singular integrals along certain compound curves as well as the related maximal operators are considered. Under rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the -mapping properties for such operators are established. Some previous results are greatly extended and improved...

本文研究粗糙核抛物型奇异积分算子及其极大算子. 借助于精细的Fourier变换估计和Littlewood-Paley理论, 并结合外插讨论, 在积分核满足球面Hardy函数条件和相当弱的径向尺寸条件下, 建立了这些算子的$L^p$有界性. 进一步, 关于沿一般光滑曲面的奇异积分算子及其极大算子的相应结果也被建立. 这些结果即使在迷向情形也是新的.

This paper is concerned with norm estimates for multilinear singular integral operators and their commutators formed by BMO functions on the weighted amalgam spaces (L v w → q ,L p ) α (ℝ n ). Some criteria of boundedness for such operators in (L v w → q ,L p ) α (ℝ n ) are given. As applications, the norm inequalities for the multilinear Calderón-...

In this paper, we consider the following integral system u(x, b) = integral(Rn) u(q)(y, b)/(b + vertical bar x - y vertical bar(lambda) dy, (0.1) which is related to the weak type convolution-Young's inequality. Under the assumption of that lambda is an element of (0, n) and 0 < q <= n/lambda, we show that system (0.1) doesn't have a positive solut...

This paper is devoted to studying the singular integral operators associated to polynomial mappings as well as the corresponding compound sub-manifolds. By imposing a restrictive condition on the kernels of the operators in the radial direction, the boundedness for such operators on Triebel-Lizorkin spaces and Besov spaces are established, provided...

In this paper, we give a characterization of the L-2 bounds for the Littlewood-Paley functions on product domains. As application, a new size condition, which implies the L-2 boundedness of the multiple parametric Marcinkiewicz integrals with rough kernels and is weaker than the previous ones, is given.

This paper is concerned with the singular integral operators along polynomial curves. The boundedness for such operators on Triebel-Lizorkin spaces and Besov spaces is established, provided the kernels satisfy rather weak size conditions both on the unit sphere and in the radial direction. Moreover, the corresponding results for the singular integr...

Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results g...

Let $L$ be a one-to-one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the weak Hardy space $WH_L^p(\mathbb{R}^n)$ associated to $L$ for $p\in (0,\,1]$ via the non-tangential square function $S_L$ and establish a w...

The authors establish the Lp -mapping properties for a class of non-isotropic singular integrals along surfaces of revolution as well as the related maximal operators, where the integral kernels are given by functions Ω in L(log+L)?α (∑) .

Multilinear commutators and iterated commutators generated by the multilinear singular integrals with non-smooth kernels and BMO functions are studied. By the weighted estimates of a class of new variant maximal operators and the sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained. In particular, some pr...

This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition F α (S m−1 × S n−1) of the kernel implies the L p -boundedness of these Marcinkiewicz integral operators for some α > 1/2 and \(\frac{1} {{2\alpha }} <...

This paper is devoted to studying the singular integrals and Marcinkiewicz integrals with mixed homogeneity along surfaces, which contain many classical surfaces as model examples, on the product domains [InlineEquation not available: see fulltext.] ([InlineEquation not available: see fulltext.]). Under rather weak size conditions of the kernels, t...

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ɛ(Sm-1×Sn-1)(ɛ=1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related Marcinkiewicz integral operators are established, provided that the lower dimensional maximal function...

In this paper, we establish the vector-valued inequalities for the commutators of singular integrals with rough kernels. In particular, our results can essentially improve some well-known results.

Let Q 2 = [0, 1]2 be the unit square in two-dimensional Euclidean space ℝ2. We study the L p boundedness of the oscillatory integral operator T α,β defined on the set ℒ(ℝ2+n ) of Schwartz test functions by $ T_{\alpha ,\beta } f(u,v,x) = \int_{Q^2 } {\frac{{f(u - t,v - s,x - \gamma (t,s))}} {{t^{1 + \alpha _1 } s^{1 + \alpha _2 } }}} e^{it - \b...

We study the weighted L p estimates (1<p<∞) for the oscillatory singular integral operator given by Tf(x)=p.v.∫ ℝ n e iΦ(x,y) b(|x-y|)Ω(x-y) |x-y| n f(y)dy· The phase function Φ has the form Φ(x,y)=∑ k=0 l P k (x)ϕ k (y-z), where P k is a real polynomial on ℝ n ,ϕ k is a real homogeneous function on ℝ n and is analytic on S n-1 ·Ω is homogeneous of...

A class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on Lp and Triebel-Lizorkin spaces is established.

In this paper, the author studies a class of non-standard commutators with higher order remainders for oscillatory singular integral operators with phases more general than polynomials. For 1 < p < ∞, the L p -boundedness of such operators are obtained provided that their kernels belong to the spaces L q (S n−1) for some q > 1.

In this paper, the author studies the k-th commutators of oscillatory singular integral operators with a BMO function and phases more general than polynomials. For 1 < p < , the -boundedness of such operators are obtained provided their kernels belong to the spaces . The results of the corresponding maximal operators are also established.

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.

Let μ be a nonnegative Radon measure satisfying the growth condition that μ(B(x,r))≤Cr n for any x∈ℝ d and r>0 and some fixed positive constants C and n with 0<n≤d. Let H atb 1,∞ (μ) be the Hardy space associated with μ which was introduced by Tolsa. In this paper, a new interpolation theorem related to H atb 1,∞ (μ) is established and the interpol...

Let Q 2 = [0, 1]2 be the unit square in two dimension Euclidean space ℝ2. We study the L p boundedness properties of the oscillatory integral operators T α,β defined on the set S(ℝ3) of Schwartz test functions f by $$ \mathcal{T}_{\alpha ,\beta } f(x,y,z) = \int_{Q^2 } {f(x - t,y - s,z - t^k s^j )e^{ - it^{ - \beta _1 } s^{ - \beta 2} } t^{ - 1 - \...

Let μ be a nondoubling measure on ℝd. A class of commutators associated with multilinear fractional integrals and RBMO(μ) functions are introduced and shown to be bounded on product of Lebesgue spaces with μ.

In this paper, the authors establish L p boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results.

By means of the method of block decompositions for kernel functions and some delicate estimates on Fourier transforms, the $L^p(\boldsymbol{R}^m\times\boldsymbol{R}^n\times\boldsymbol{R})$-boundedness of the multiple Marcinkiewicz integral is established along a continuous surface with rough kernel for some $p>1$. The condition on the integral kern...

In this paper we prove the Lp-boundedness of some Marcinkiewicz integral operators along surfaces of revolution. Some size conditions implying the Lp(Rn+1) boundedness of these operators for some fixed 1p∞ are obtained.

This paper is devoted to the study of the Lp -mapping properties of the higher order commutators μkΩ,a, μ*,k Ω,λ ,a and μkΩ,S ,a, which are formed respectively by a BMO (ℝn) function a (x ) and a class of rough Marcinkiewicz integral operators μΩ, μ*Ω,λ and μΩ,S related to the Littlewood–Paley g -function, the Littlewood–Paley g*λ -function and the...

This paper is concerned with giving some rather weak size conditions implying the L p boundedness of the multiple Marcin-kiewicz integrals for some fixed 1 < p < ∞, which essentially im-prove and extend some known results.

This paper is devoted to the study on the Lp -mapping properties for certain singular integral operators with rough kernels and related Littlewood–Paley functions along “polynomial curves” on product spaces ℝm × ℝn (m ≥ 2, n ≥ 2). By means of the method of block decomposition for kernel functions and some delicate estimates on Fourier transforms, t...

For the multilinear oscillatory singular integral operators T A 1 ,A 2 ,⋯,A r defined by T A 1 ,A 2 ,⋯,A r f(x)=p.v.∫ ℝ n e iP(x,y) Ω(x-y) |x-y| n+M ∏ s=1 r R m s +1 (A 3 ;x,y)f(y)dy,n≥2, where P(x,y) is a nontrivial and real-valued polynomial defined on ℝ n ×ℝ n , Ω(x) is homogeneous of degree zero on ℝ m , A s (x) has derivatives of order m S in...

This paper is devoted to the study on the Lp-mapping properties of Marcinkiewicz integral operators with rough kernels along “polynomial curves” on \mathbbRn .\mathbb{R}^n . The Lp (\mathbbRn )L^p (\mathbb{R}^n ) boundedness of the Marcinkiewicz integrals for some fixed 1p

Let µ Ω.b be the commutator generalized by the n-dimensional marcinkiewicz integral µ Ω and a function \(b \in BMO (R^n )\) . It is proved that µ Ω.b is bounded from the Hardy space H 1 (R n) into the weak L 1 (R n) space.

The author studies the commutators generated by a suitable function a(x) on ℝ n and the oscillatory singular integral with rough kernel Ω(x)|x| n and polynomial phase, where Ω is homogeneous of degree zero on R n, and a(x) is a BMO function or a Lipschitz function. Some mapping properties of these higher order commutators on L p(R n), which are ess...

This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(\rz)$ boundedness of the multilinear oscillat...

In this paper, for the multilinear oscillatory singular integral operators T-A defined by [GRAPHICS] where P(x, y) is a nontrivial and real-valued polynomial defined on R-n x R-n, Omega(x) is homogeneous of degree zero on R-n, A(x) has derivatives of order m in <(&ULambda;)over dot> (0 < beta < 1), Rm+1 (A; x, y) denotes the (m + 1)th remainder of...

In this paper, the L 2 -boundedness of a class of parametric Marcinkiewicz integral μ Ω,h ρ with kernel function Ω in B q 0,0 (S n−1) for for some q>1, and the radial function h(x) ∈ l ∞ (L s )(R+) for 1<s≤∞ are given. The L p (R n ) (2≤p<∞) boundedness of mW * ,\backprime hr .l\mu _\Omega ^* ,{}^\backprime h^\rho .\lambda and mW r ,h...

By the method of block decomposition for a kernel function and some precise inequalities concerning polynomials, the authors give a verifiable necessary and sufficient condition for the boundedness of a class of oscillatory singular integrals with rough kernels on L p (ℝ n ). In addition, the authors also discuss the weighted L p -boundedness for h...

In this paper we study the average δ-K width and the average δ-linear width of the unit ball of l 1∞ (ℝ) in l 2∞ (ℝ). The exact values of these widths are calculated and an optimal subspace with the optimal linear operator (for the δ-linear width) are identified.