Title:

Tb theorem for weighted Besov spaces and Triebel-Lizorkin spaces on homogeneous spaces

作者：

刘金瑞, 郑涛涛, 肖燕梅

刘金瑞,郑涛涛,肖燕梅

Author(s):

LIU Jinrui, ZHENG Taotao, XIAO Yanmei

LIU Jinrui, ZHENG Taotao, XIAO Yanmei

单位:

(浙江科技大学 理学院,杭州 310023)

Unit:

(School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, Zhejiang, China)

关键词:

加权Besov空间; 加权Triebel-Lizorkin空间; Plancherel-P?lya特征刻画; 仿增长函数; Tb定理

加权Besov空间; 加权Triebel-Lizorkin空间; Plancherel-P?lya特征刻画; 仿增长函数; Tb定理

分类号:

O174.2

DOI:

10.3969/j.issn.1671-8798.2024.01.001

文献标识码:

A

摘要:

【目的】齐型空间自然地包含了欧氏空间Rⁿ、光滑紧Riemann流形及Lipschitz区域的边界等,拟在齐型空间上建立奇异积分算子在加权Besov空间与Triebel-Lizorkin空间上有界的Tb定理。【方法】通过离散Calderón再生公式和几乎正交估计建立加权Besov空间与加权Triebel-Lizorkin空间的Plancherel-P?lya特征刻画,以保证函数空间的范数独立于恒等逼近的选取。【结果】获得了齐型空间上Calderón-Zygmund奇异积分算子在加权Besov空间及Triebel-Lizorkin空间上有界的充分条件。【结论】将欧氏空间上的Calderón-Zygmund奇异积分理论延拓到更广的齐型空间上,为奇异积分算子在函数空间上有界提供了判定方法。

参考文献
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备注/Memo:

收稿日期:2023-06-18
基金项目:国家自然科学基金项目(11626213); 浙江省自然科学基金项目(LQ17A010002)
通信作者:郑涛涛(1984— ),男,江西省上饶人,副教授,博士,主要从事调和分析及统计分析研究。E-mail:zhengtao@zust.edu.cn。