数学物理学报(英文版) ›› 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

邓浏睿|李中凯|马柏林|伍火熊*   

  1. 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
  • 收稿日期:2009-02-10 修回日期:2011-04-15 出版日期:2011-09-20 发布日期:2011-09-20
  • 通讯作者: 伍火熊,huoxwu@xmu.edu.cn E-mail:dengzimu@yahoo.com.cn;lizk@mail.cnu.edu.cn;blma@mail.zjxu.edu.cn;huoxwu@xmu.edu.cn
  • 基金资助:

    Supported by the NSFC (10771054, 10971141, 11071200) and the NFS of Beijing (1092004) and the NFS of Fujian Province (2010J01013).

ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES

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

  1. 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).

摘要:

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm−1
× Sn−1) (ε = 1 or 2) supported by hyper-surfaces. The Lp 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 Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.

关键词: multiple singular integral, Marcinkiewicz integral, maximal function, hyper-surface, rough kernel

Abstract:

In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm−1
× Sn−1) (ε = 1 or 2) supported by hyper-surfaces. The Lp 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 Lq(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

中图分类号: 

  • 42B20