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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (12): 45-54.doi: 10.6040/j.issn.1671-9352.0.2021.685

• • 上一篇    

极大变指标Herz空间上的参数型粗糙核Littlewood-Paley算子

史鹏伟,陶双平*   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2022-12-05
  • 作者简介:史鹏伟(1997— ),男,硕士研究生,研究方向为调和分析. E-mail:Shipengwei2331@163.com *通信作者简介:陶双平(1964— ),男,教授,博士生导师,研究方向为调和分析及其应用. E-mail:taosp@nwnu.edu.cn
  • 基金资助:
    国家自然科学基金项目(12161080)

Parameterized Littlewood-Paley operators with rough kernel on grand variable Herz spaces

SHI Peng-wei, TAO Shuang-ping*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-12-05

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摘要： 借助变指标Lebesgue空间上的有界性,利用函数分层分解和实变技巧,得到了参数型粗糙核Marcinkiewicz积分、面积积分和 Littlewood-Paley g*λ函数在极大变指标Herz空间上的有界性。同时也证明了面积积分和Littlewood-Paley g*λ函数高阶交换子的有界性。

关键词: 极大变指标Herz空间, 粗糙核, 参数型Littlewood-Paley算子, 高阶交换子

Abstract: With the help of the boundedness of the Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of the parameterized Marcinkiewicz integral, the area integral and Littlewood-Paley g*λ function with rough kernel is obtained on grand variable Herz spaces. Meanwhile, the boundedness of higher order commutators generated by the area integral and Littlewood-Paley g*λ function is also proved on grand variable Herz spaces.

Key words: grand variable Herz space, rough kernel, parameterized Littlewood-Paley operator, higher order commutator

中图分类号: 

  • O174.2
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