数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 1026-1039.

• 论文 • 上一篇    下一篇

沿复合曲线的粗糙核参数型Marcinkiewicz积分算子的有界性

刘风|伍火熊|张代清*   

  1. 厦门大学数学科学学院 |厦门 |361005
  • 收稿日期:2012-12-24 修回日期:2014-03-10 出版日期:2014-08-25 发布日期:2014-08-25
  • 通讯作者: 张代清,zhangdaiqing2011@163.com E-mail:liufeng860314@163.com; huoxwu@xmu.edu.cn; zhangdaiqing2011@163.com
  • 基金资助:

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

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.

摘要:

研究沿复合曲线的粗糙核参数型Marcinkiewicz积分算子, 在积分核满足相当弱的尺寸条件下, 建立了这些算子的Lp有界性. 作为应用, 相应于面积积分和Littlewood-Paley-g*λ函数的参数型Marcinkiewicz积分算子的Lp有界性也被给出.

关键词: 参数型Marcinkiewicz积分, 复合映射, 粗糙核, Fourier变换估计

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

中图分类号: 

  • 42B15