Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 1026-1039.

• Articles • Previous Articles     Next Articles

Parametric Marcinkiewicz Integrals with Rough Kernels Supported by Compound Subvarieties

 LIU Feng, WU Huo-Xiong, ZHANG Dai-Qing*   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005
  • Received:2012-12-24 Revised:2014-03-10 Online:2014-08-25 Published:2014-08-25
  • Contact: ZHANG Dai-Qing,zhangdaiqing2011@163.com E-mail:liufeng860314@163.com; huoxwu@xmu.edu.cn; zhangdaiqing2011@163.com
  • Supported by:

    国家自然科学基金(G11071200, 11371295)和福建省自然科学基金(2010J01013)资助.

Abstract:

In this paper, we establish the Lp boundedness for a class of rough parametric Marcinkiewicz integral operators
associated with polynomial compound mappings, under rather weaker size conditions on the kernels, which essentially improve and generalize certain previous results. As applications, the Lp bounds of the corresponding parametric Marcinkiewicz integral operators related to area integrals and Littlewood-Paley g*λ functions are also obtained.

Key words: Parametric Marcinkiewicz integrals, Compound mappings, Rough kernels, Fourier transform estimates

CLC Number: 

  • 42B15
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