ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

doi:10.1016/S0252-9602(11)60383-4

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 2081-2098.doi: 10.1016/S0252-9602(11)60383-4

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ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

DENG Liu-Rui, LI Zhong-Kai, MA Bo-Lin, WU Huo-Xiong^*

College of Mathematics and Econometrics, Hunan University, Changsha 410082, China； School of Mathematical Sciences, Capital Normal University, Beijing 100048, China； College of Science and Information Engineering, Jiaxing University, Jiaxing 314001, China； School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2009-02-10 Revised:2011-04-15 Online:2011-09-20 Published:2011-09-20
Contact: WU Huo-Xiong，huoxwu@xmu.edu.cn E-mail:dengzimu@yahoo.com.cn；lizk@mail.cnu.edu.cn；blma@mail.zjxu.edu.cn；huoxwu@xmu.edu.cn
Supported by:
Supported by the NSFC (10771054, 10971141, 11071200) and the NFS of Beijing (1092004) and the NFS of Fujian Province (2010J01013).

Abstract

Abstract:

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)^ε(S^m⁻¹× Sⁿ⁻¹) (ε = 1 or 2) supported by hyper-surfaces. The L^p bounds for such singular integral operators as well as the related
Marcinkiewicz integral operators are established, provided that the lower dimensional max-imal function is bounded on L^q(R³) for all q > 1. The condition on the integral kernels is known to be optimal.

Key words: multiple singular integral, Marcinkiewicz integral, maximal function, hyper-surface, rough kernel

CLC Number:

42B20

DENG Liu-Rui, LI Zhong-Kai, MA Bo-Lin, WU Huo-Xiong. ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES[J].Acta mathematica scientia,Series B, 2011, 31(5): 2081-2098.

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ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

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