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L^2（R^n） Boundedness for a Class of Multilinear Singular Integral Operators

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Acta Mathematica Sinica,English Series 2003年第2期19卷 397-404页

作者： GuoEnHU DepartmentofAppliedMathdematics UniversityofInformationEngineeringP.O.Box1001-747Zhengzhou450002P.R.China

The L^2(A^n) boundedness for the multilinear singular integral operators defined by$T_A f\left( x \right) = \int_{Ropf^n } {{{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + 1} }}} \left( {A\left( x \right) - A\left( y \right) - \nabla A\left( y \right)\left( {x - y} \right)} \right)f\left( y \right)dy$is considered, whereQ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(A^n). A sufficient condition based on the fourier transform estimate and implying the L^2(A^n) boundedness for the multilinear operator TA is given.

关键词： Multilinear singular integral operator BMO(ℝ n ) fourier transform estimate 42B20

On Multiple Singular Integrals along Polynomial Curves with Rough Kernels

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Acta Mathematica Sinica,English Series 2008年第2期24卷 177-184页

作者： Huo Xiong WU Shan Zhi YANG School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.

关键词： singular integral product domain rough kernel Littlewood-Paley theory fourier transform estimate

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Rough Marcinkiewicz integrals along certain smooth curves

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Frontiers of Mathematics in China 2012年第5期7卷 857-872页

作者： Bolin MA Huoxiong WU Xiating ZHAO College of Mathematics and Information Engineering Jiaxing University Jiaxing 314001 China School of Mathematical Sciences Xiamen University Xiamen 361005 China Third Middle-School of Zhuhai City Zhuhai 519000China

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 Fa（S^m-1 × S ^n-1） of the kernel implies the L P-boundedness of these Marcinklewicz integral operators for 1 some a 〉 1/2 and 1 ＋ 1/2a 〈 p 〈 1 ＋ 2a, which is an essential improvement of certain previous results.

关键词： Marcinkiewicz integral rough kernel smooth curve Littlewood-Paley theory fourier transform estimate

COMPACTNESS FOR THE COMMUTATOR OF BOCHNER-RIESZ OPERATOR

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Acta Mathematica Scientia 2017年第5期37卷 1373-1384页

作者：卜瑞陈杰诚胡国恩 Department of Mathematics Qingdao University of Science and TechnologyQingdao 266061China Department of Mathematics Zhejiang Normal UniversityJinhua 321003China Department of Applied Mathematics Zhengzhou Information Science and Technology InstituteZhengzhou 450002China

Let α ∈0,(n-1)/2 and T~α be the Bochner-Riesz operator of order α. In this paper, for n = 2 and n ≥ 3, the compactness on Lebesgue spaces and Morrey spaces are considered for the commutator of Bochner-Riesz opera... 详细信息

关键词： Bochner-Riesz operator commutator compact operator fourier transform estimate

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On　a　Multiple　Singular　Integral　Operator

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Communications in Mathematical Research 1997年第2期 11-19页

作者：胡国恩

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关键词： Multiple Singular Integral Operator fourier transform estimate Littlewood Paley Theory