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ABSTRACT: We study the boundedness of some sublinear operators on weighted Morrey
spaces under certain size conditions. These conditions are satisfied by most of
the operators in harmonic analysis, such as the Hardy-Littlewood maximal
operator, Calder\'{o}n-Zygmund singular integral operator, Bochner-Riesz means
at the critical index, oscillatory singular operators, singular integral
operators with oscillating kernels and so on. As applications, the regularity
in weighted Morrey spaces of strong solutions to nondivergence elliptic
equations with VMO coefficients are established.
08/2012;
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ABSTRACT: In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
Keywords
n-dimensional rough Hardy operator–commutator–central BMO space–central Morrey space
Science China Mathematics 05/2012; 54(1):95-104. · 0.33 Impact Factor
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ABSTRACT: In this paper, we study the weighted norm inequalities for commutators formed by a class of one-sided oscillatory integral
operators and functions in one-sided BMO spaces.
KeywordsCommutator–one-sided oscillatory integral–BMO–one-sided weight
Frontiers of Mathematics in China 04/2012; 6(3):507-516. · 0.55 Impact Factor
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ABSTRACT: The operator norms of weighted Hardy operators on Morrey spaces are worked out. The other purpose of this paper is to establish
a sufficient and necessary condition on weight functions which ensures the boundedness of the commutators of weighted Hardy
operators (with symbols in BMO(ℝ
n
)) on Morrey spaces.
KeywordsWeighted Hardy operator-BMO-commutator-Morrey space
MSC42B25-26D15-42B99
Frontiers of Mathematics in China 04/2012; 5(3):531-539. · 0.55 Impact Factor
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ABSTRACT: It is proved that both oscillatory integral operators and fractional
oscillatory integral operators are bounded on weighted Morrey spaces. The
corresponding commutators generated by $BMO$ functions are also considered.
11/2011;
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ABSTRACT: We set up some weighted norm inequalities for fractional oscillatory integral
operators. As applications, the corresponding results for commutators formed by
$BMO(\mathbb{R}^{n})$ functions and the operators are established.
11/2011;
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ABSTRACT: The purpose of this paper is to establish the weighted norm inequalities of
one-sided oscillatory integral operators by the aid of interpolation of
operators with change of measures.
06/2011;
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ABSTRACT: We get the sharp bound for weak type $(1,1)$ inequality for $n$-dimensional
Hardy operator. Moreover, the precise norms of generalized Hardy operators on
the type of Campanato spaces are obtained. As applications, the corresponding
norms of the Riemann-Liouville integral operator and $n$-dimensional Hardy
operator are deduced.
06/2011;
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ABSTRACT: In this paper, it is proved that the higher dimensional Hardy operator is
bounded from Hardy space to Lebesgue space. The endpoint estimate for the
commutator generated by Hardy operator and (central) BMO function is also
discussed.
06/2011;
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ABSTRACT: We consider one-sided weight classes of Muckenhoupt type and study the
weighted weak type (1,1) norm inequalities of a class of one-sided oscillatory
singular integrals with smooth kernel.
05/2011;
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ABSTRACT: In this paper we get the sharp estimates of the $p$-adic Hardy and
Hardy-Littlewood-P\'olya operators on $L^q(|x|^{\alpha}_pdx)$. Also, we prove
that the commutators generated by the $p$-adic Hardy operators
(Hardy-Littlewood-P\'olya operators) and the central BMO functions are bounded
on $L^q(|x|^{\alpha}_pdx)$, more generally, on Herz spaces.
05/2011;
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ABSTRACT: LetHa,b be the commutator generated by the generalized Hardy operator and the CMO function. The (Lp, Lp) boundedness of Ha,b is discussed in this paper. Furthermore, the authors consider the boundedness of Ha,b on the weighted homogeneous Herz spaces (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematische Nachrichten 05/2009; 282(6):832 - 845. · 0.68 Impact Factor
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ABSTRACT: In this paper, the boundedness of the commutator generated by strongly singular Calderón-Zygmund operator and a Lipschitz
function is discussed on the classical Hardy spaces and the Herz-type Hardy spaces. The authors also get the boundedness of
the strongly singular Calderón-Zygmund operator itself and the commutator generated by strongly singular Calderón-Zygmund
operator and a BMO function on the Herz-type Hardy spaces.
Integral Equations and Operator Theory 02/2007; 57(3):381-396. · 0.63 Impact Factor
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ABSTRACT: In this paper, the boundedness of Toeplitz operator T
b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε
[(L)\dot] b0 \dot \Lambda _{\beta _0 }
(ℝn) is discussed from L
p(ℝn) to L
q(ℝn),
\tfrac1q = \tfrac1p - \tfracb0 n\tfrac{1}{q} = \tfrac{1}{p} - \tfrac{{\beta _0 }}{n}
, and from L
p(ℝn) to Triebel-Lizorkin space
[(F)\dot]pb0 ,¥\dot F_p^{\beta _0 ,\infty }
. We also obtain the boundedness of generalized Toeplitz operator Θ
α0
b
from L
p(ℝn) to L
q(ℝn),
\tfrac1q = \tfrac1p - \tfraca0 + b0 n\tfrac{1}{q} = \tfrac{1}{p} - \tfrac{{\alpha _0 + \beta _0 }}{n}
. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator
T
b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L
p(ℝn), 1 < p < ∞.
Science in China Series A Mathematics 07/2006; 49(8):1048-1064. · 0.70 Impact Factor
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ABSTRACT: In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey
and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderón-Zygmund
operator can be obtained.
Analysis in Theory and Applications 01/2006; 22(4):387-400.
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ABSTRACT: In this paper, the authors study a class of multilinear singular integral operators on product of Hardy spaces. The boundedness of another class of multilinear singular integral operators is also discussed on product of Herz-type spaces. Moreover, as their special cases, the corresponding results of multilinear fractional integral operator and multilinear Calder\'on-Zygmund operator can be obtained, respectively.
