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（L^p,L^q） Estimates for Multilinear Oscillatory Singular Integralswith Smooth Phases

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Acta Mathematica Sinica,English Series 2003年第4期19卷 645-654页

作者： ShanZhenLU GuiPingTAO DepartmentofMathematics BeijingNormalUniversityBeijing100875P.R.China

In this paper, the authors establish the weighted (L^p, L^q) estimates for aclass of multilinear oscillatory singular integrals with smooth phases. Certain endpoint estimatesare also considered.

关键词： multilinear oscillatory singular integral lebesgue space weight BMO

Calderón-Zygmund-Type Operators on Weighted Weak Hardy spaces over R^n

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Acta Mathematica Sinica,English Series 2000年第1期16卷 141-160页

作者： Tongseng Quek Dachun Yang Department of Mathematics National University of SingaporeSingapore 119260Republic of Singapore Department of Mathematics Beijing Normal UniversityBeijing 100875P.R.China

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted lebesgue spaces,weighted weak lebesgue spaces,weighted Hardy spaces and weighted weak Hardy *** sharpness ... 详细信息

关键词： Calderón-Zygmund operator lebesgue space Weak lebesgue space Hardy space Weak Hardy space Atom Weight

BOUNDEDNESS OF RIESZ POTENTIALS IN NONHOMOGENEOUS spaceS

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Acta Mathematica Scientia 2008年第2期28卷 371-382页

作者：胡国恩孟岩杨大春 Department of Applied Mathematics University of Information Engineering School of Information Renmin University of China School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education

For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.

关键词： Riesz potential lebesgue space Hardy space RBMO space boundedness,non-doubling measure

Some Oscillatory Singular Integrals on Herz-type spaces (Ⅱ)

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 365-376页

作者： Gary Sampson Department of Mathematics Auburn University AuburnAL 36849-5310USA

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the lebesgue spaceL1(Rn).

关键词： Oscillatory singular integral phase lebesgue space Herz space Beurling algebra Hardy space

A NOTE TO OSCILLATORY SINGULAR INTEGRALS ON HERZ-TYPE spaceS

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Analysis in Theory and Applications 2003年第1期19卷 37-46页

作者： G.Sampson XuJingshi AuburnUniversity U.S.A HunanUniversity China/ChangshaUniversityofElectricPowerChina

In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.

关键词： oscillatory singular integral phase lebesgue space Herz space Beurling algebra Hardy space

Boundedness of Marcinkiewicz integrals and their commutators in H1（Rn×Rm）

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Science China Mathematics 2006年第6期 770-790页

作者： YANG Dachun & ZHOU Yuan School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn×Rm) to the lebesgue space L1(Rn×Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn×Rm) to the L... 详细信息

关键词： Marcinkiewicz integral commutator Lipschitz function atom Hardy space lebesgue space boundedness.

Uniform (L~P, L~q) boundedness of multilinear oscillatory singular integrals

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Progress in Natural Science:Materials International 2000年第10期10卷 26-35页

作者：陆善镇吴强杨大春 Beijing 100875 Beijing Normal University China Department of Mathematics

A class of multilinear oscillatory singular integrals with smooth phases is studied. And their uniform boundedness on lebesgue space is proved.

关键词： multilinear oscillatory singular integral lebesgue space weight BMO.