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Weighted Norm Inequalities with General Weights for the Commutator of Calderón

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Acta Mathematica Sinica,English Series 2013年第3期29卷 505-514页

作者： Guo En HU Yue Ping ZHU Department of Applied Mathematics Zhengzhou Information Science and Technology Institute School of Science Nantong University

In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1 （Rn） ×..…… L1 （Rn） to L1/m,∞（Rn）, and the associated kernel K（x; yl,.. , Ym） enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of CalderSn.

关键词： Approximation to the identity weighted norm inequality singular integral operator max-imal operator non-smooth kernel

Mapping Properties of Certain Oscillatory integrals on Modulation Spaces

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Acta Mathematica Sinica,English Series 2017年第12期33卷 1647-1658页

作者： Mei Fang CHENG Hui Hui LIU Ai Wen SUN School of Mathematical and Computer Sciences Anhui Normal University Wuhu 241002 P. R. China

Suppose β1 〉 α1 ≥ 0, β2 〉 α2 ≥ 0 and （k,j） ∈ R^2. In this paper, we mainly investigate the mapping properties of the operator Tα,βf（x,y,z）=∫Q^2f（x-t,y-s,z-t^ks^j）e^-2πit-β1s-β2t^-1-α1s^-1-α2 dtd... 详细信息

关键词： Modulation space singular integral operator Wiener amalgam space

singular integral EQUATIONS WITHCOMPLEX TRANSLATIONS

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Acta Mathematica Scientia 1999年第4期19卷 469-480页

作者：杜金元胡继承 Department of Mathematics Wuhan University Wuhan 430072 China

In this paper, a class of singular integral equations with complex translations is discussed. By using the Plemelj projection method the authors reduce them to the boundary value problem of analytic functions in A(+)(H) over cap(0) with upper translation and the boundary value problem of analytic functions in A-(H) over cap(0) with lower translation, which are solved here.

关键词： singular integral equation singular integral operator singular projection operator upper translation lower translation

ON THE EXISTENCE OF ALMOST GLOBAL WEAK SOLUTION TO MULTIDIMENSIONAL VLASOV-POISSON EQUATION

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Chinese Annals of Mathematics,Series B 1998年第3期19卷 381-390页

作者： Z HZNG PING QIU QINGJIU 南京大学数学系江苏南京

The authors prove the existence of almost global weak solution to multidimensional Vlasov Poisson equation with a class of Randon measure as initial data.

关键词： Vlasov Poisson equation Almost global weak solution singular integral operator

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一类沿径向曲面的奇异积分算子的弱型估计

Northeastern Mathematical Journal 1995年第2期11卷 191-198页

作者：陈理元王斯雷

Let : R→R denote a reasonably smooth curve. The singular integral operators and maximal functions along a radial surface S= (t, ,(t)) are defined by where n≥3, b is a bounded radial function, and Ω∈Lη(Sn-2) for some q>1 is homogeneous of degree zero and satisfies the cancellation property (i. e., sn-2Ω(y)dσ(y)=0). Then for a kind of radial surfaces, the operators T, T and M , M defined above are bounded from the space L(logl.)ato weak L1 for some α>0.

关键词： operator singular integral operator Weak Type Estimate

Weak Orlicz spaces:Some basic properties and their applications to harmonic analysis

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Science China Mathematics 2013年第4期56卷 789-802页

作者： LIU PeiDe WANG MaoFa School of Mathematics and Statistics Wuhan University

We study some basic properties of weak Orlicz spaces and their applications to harmonic *** first discuss the absolute continuity of the quasi-norm and its normality,then prove the boundedness of several maximal *** also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz *** applications,the weak type analogues of several classical inequalities in harmonic analysis is obtained.

关键词： weak Orlicz space normality maximal operator interpolation theorem singular integral operator

Wavelet shrinkage estimators of Calderón-Zygmund operators with odd kernels

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Science China Mathematics 2014年第9期57卷 1983-1991页

作者： CHEN Heng WU JiTao Department of Mathematics Beijing University of Aeronautics and Astronautics

Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,*** Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of *** the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this *** almost everywhere convergence and norm convergence of the proposed estimators are established.

关键词： wavelets shrinkage singular integral operator non-standard form maximal operator

Characterizations of Some operators on the Vanishing Weak Morrey Type Spaces

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Journal of Mathematical Research with Applications 2018年第2期38卷 183-193页

作者： Pinhong LONG Huili HAN Hua HU School of Mathematics and Statistics Ningxia University

In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces... 详细信息

关键词： weight Hardy operator maximal operator potential operator singular integral operator weak Morrey space

A Generalized Marcinkiewicz Interpolation Theorem and Its Applications

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Wuhan University Journal of Natural Sciences 1996年第1期1卷 17-19页

作者： Liu Peide Wei Wenzhan (Departmant of Mathematics, Wuhan University, Wuhan 430072, China) Department of Mathematics Wuhan University Wuhan China

Using a simple method,we generalize Marcinkiewicz interpolation theorem to *** Orlicz space and apply it to several important theorems in harmonic analysis.

关键词： Marcinkiewicz interpolation theorem Orlicz space singular integral operator