数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 11-25.doi: 10.1007/s10473-019-0102-0

• 论文 • 上一篇    下一篇

LIMITING WEAK-TYPE BEHAVIORS FOR CERTAIN LITTLEWOOD-PALEY FUNCTIONS

侯宪明, 伍火熊   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2018-01-29 修回日期:2018-05-09 出版日期:2019-02-25 发布日期:2019-03-13
  • 通讯作者: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
  • 作者简介:Xianming HOU,houxianming37@163.com
  • 基金资助:
    The research was supported by the NSFC (11771358, 11471041).

LIMITING WEAK-TYPE BEHAVIORS FOR CERTAIN LITTLEWOOD-PALEY FUNCTIONS

Xianming HOU, Huoxiong WU   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2018-01-29 Revised:2018-05-09 Online:2019-02-25 Published:2019-03-13
  • Contact: Huoxiong WU E-mail:huoxwu@xmu.edu.cn
  • Supported by:
    The research was supported by the NSFC (11771358, 11471041).

摘要: In this paper, we establish the following limiting weak-type behaviors of Littlewood Paley g-function gφ:for nonnegative function fL1(Rn),

where ft(x)=t-nf(t-1x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying Lαq-Dini condition are also given.

关键词: limiting behaviors, weak-type bounds, Littlewood-Paley g-functions, Marcinkiewicz integrals, Lαq-Dini conditions

Abstract: In this paper, we establish the following limiting weak-type behaviors of Littlewood Paley g-function gφ:for nonnegative function fL1(Rn),

where ft(x)=t-nf(t-1x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying Lαq-Dini condition are also given.

Key words: limiting behaviors, weak-type bounds, Littlewood-Paley g-functions, Marcinkiewicz integrals, Lαq-Dini conditions