数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 241-256.doi: 10.1007/s10473-021-0114-4

• 论文 • 上一篇    下一篇

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

刘荣辉1, 刘风2, 伍火熊1   

  1. 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
    2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
  • 收稿日期:2019-10-09 修回日期:2020-01-05 出版日期:2021-02-25 发布日期:2021-04-06
  • 通讯作者: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
  • 作者简介:Ronghui LIU,E-mail:liuronghuimath@126.com;Feng LIU,E-mail:FLiu@sdust.edu.cn
  • 基金资助:
    The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

ON THE MIXED RADIAL-ANGULAR INTEGRABILITY OF MARCINKIEWICZ INTEGRALS WITH ROUGH KERNELS

Ronghui LIU1, Feng LIU2, Huoxiong WU1   

  1. 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
    2. College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
  • Received:2019-10-09 Revised:2020-01-05 Online:2021-02-25 Published:2021-04-06
  • Contact: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
  • About author:Ronghui LIU,E-mail:liuronghuimath@126.com;Feng LIU,E-mail:FLiu@sdust.edu.cn
  • Supported by:
    The authors were partly supported by the NSFC (11771358, 11701333, 11871101).

摘要: This paper studies the mixed radial-angular integrability of parametric Marcinki-ewicz integrals along "polynomial curves". Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

关键词: Marcinkiewicz integrals, rough kernels, mixed radial-angular spaces

Abstract: This paper studies the mixed radial-angular integrability of parametric Marcinki-ewicz integrals along "polynomial curves". Under the assumption that the kernels satisfy certain rather weak size conditions on the unit sphere with radial roughness, the authors prove that such operators are bounded on the mixed radial-angular spaces. Meanwhile, corresponding vector-valued versions are also obtained.

Key words: Marcinkiewicz integrals, rough kernels, mixed radial-angular spaces

中图分类号: 

  • 42B20