Zhuoping Ruan

Zhuoping Ruan
Nanjing University | NJU · Department of Mathematics

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12
Publications
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162
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Publications

Publications (12)
Article
Full-text available
We prove the local existence and uniqueness of minimal regularity solutions $u$ of the semilinear generalized Tricomi equation $\partial_t^2 u-t^m \Delta u =F(u)$ with initial data $(u(0,\cdot), \partial_t u(0,\cdot)) \in \dot{H^{\gamma}}(\mathbb R^n) \times \dot{H}^{\gamma-\frac2{m+2}}(\mathbb R^n)$ under the assumption that $|F(u)|\lesssim |u|^\k...
Article
In [19-20], we have established the existence and singularity structures of low regularity solutions to the semilinear generalized Tricomi equations in the degenerate hyperbolic regions and to the higher order degenerate hyperbolic equations, respectively. In the present paper, we shall be concerned with the low regularity solution problem for the...
Article
Full-text available
In this paper, we use the discrete Littlewood-Paley-Stein analysis to get the duality result of the weighted product Hardy space for arbitrary number of parameters under a rather weak condition on the product weight w∈A ∞ (ℝ n 1 ×⋯×ℝ n k ). We will show that for any k≥2,(H w p (ℝ n 1 ×⋯×ℝ n k )) * =CMO w p (ℝ n 1 ×⋯×ℝ n k ) (a generalized Carleson...
Article
In this paper, we obtain the boundedness of singular integral operators T in Journé’s class on weighted multiparameter Hardy spaces $H^{p}_{w}$ of arbitrary k number of parameters (k≥3) under the assumption that $T^{\ast}_{i}(1)=0$ , i=1,…,k, and the kernel of T has a regularity of order ϵ>0, where $w \in A_{r}(\Bbb{R}^{n_{1}}\times \cdots \t...
Article
This paper is a continuation of our previous work [21], where we have established that, for the second-order degenerate hyperbolic equation (\p_t^2-t^m\Delta_x)u=f(t,x,u), locally bounded, piecewise smooth solutions u(t,x) exist when the initial data (u,\p_t u)(0,x) belongs to suitable conormal classes. In the present paper, we will study low regul...
Article
This article concerns nonconvolutional type operators (also known as Journéʼs type operators) associated with a multiparameter family of dilations given by (x1,x2,…,xm)→(δ1x1,δ2x2,…,δmxm)(x1,x2,…,xm)→(δ1x1,δ2x2,…,δmxm) where x1∈Rn1,x2∈Rn2,…,xm∈Rnmx1∈Rn1,x2∈Rn2,…,xm∈Rnm and m⩾3m⩾3. We are especially interested in the boundedness of such operators on...
Article
It is well known that standard Calderón-Zygmund singular integral operators with isotropic and nonisotropic homogeneities are bounded on the classical Hp(ℝm) and nonisotropic Hhp(ℝm), respectively. In this paper, we develop a new Hardy space theory and prove that the composition of two Calderón-Zygmund singular integral operators with different hom...
Article
Full-text available
In this paper, we are concerned with the local existence and singularity structure of low regularity solutions to the semilinear generalized Tricomi equation $\p_t^2u-t^m\Delta u=f(t,x,u)$ with typical discontinuous initial data $(u(0,x), \p_tu(0,x))=(0, \vp(x))$; here $m\in\Bbb N$, $x=(x_1, ..., x_n)$, $n\ge 2$, and $f(t,x,u)$ is $C^{\infty}$ smoo...
Article
Recently, Han and Lu [HL] developed a discrete Littlewood- Paley-Stein analysis and multi-parameter Hardy space theory associated with isotropic flag singular integral operators initially studied by Muller- Ricci-Stein [MRS] and Nagel-Ricci-Stein [NRS]. The purpose of this paper is to carry out the multi-parameter Hardy space theory associated with...
Article
In this paper, we use the idea of the discrete Littlewood–Paley theory developed by Han and Lu to carry out the three-parameter weighted Hardy spaces theory under a rather weak condition on the product weight (w∈A∞) and obtain the boundedness of singular integral operators on the weighted Hardy spaces.
Article
In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces $$ H^p \left( {R^{n_1 } \times \cdots \times R^{n_k } } \right) $$ of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators on $$ H^p \left( {R^{n_1 } \times \cdots \times...
Article
We apply discrete multiparameter Littlewood-Paley-Stein analysis, developed by Han and Lu [5], and results in [11] on the multi-parameter Hardy space theory associated with non-isotropic flag singular integral to get the corresponding dual space theory as well as Calderón-Zygmund decomposition and the interpolation theorem on flag Hardy space assoc...

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