Boundedness of multi-parameter Fourier multiplier operators on Triebel-Lizorkin and Besov-Lipschitz spaces

被引：15
|
作者：
Chen, Lu [1 ]
Lu, Guozhen [2 ]
Luo, Xiang [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 134卷
基金：
美国国家科学基金会;
关键词：
Multi-parameter Fourier multiplier; Multi-parameter Triebel-Lizorkin spaces; Multi-parameter Besov-Lipschitz spaces; Strong maximal functions; Littlewood-Paley decomposition; CALDERON-ZYGMUND THEORY; SINGULAR-INTEGRALS; JOURNES CLASS; FLAG KERNELS;
D O I：
10.1016/j.na.2015.12.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main purpose of this paper is three-fold. First, we prove that under the limited smoothness conditions, multi-parameter Fourier multiplier operators are bounded on multi-parameter Triebel-Lizorkin and Besov-Lipschitz spaces by the Littlewood-Paley decomposition and the strong maximal operator. Second, we offer a different and more direct method to deal with the boundedness instead of transforming Fourier multiplier operators into multi-parameter Calderon-Zygmund operators. Third, we also prove the boundedness of multi-parameter Fourier multiplier operators on weighted multi-parameter Triebel-Lizorkin and Besov-Lipschitz spaces when the Fourier multiplier is only assumed with limited smoothness. (C) 2016 Elsevier Ltd. All rights reserved.
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页码：55 / 69
页数：15
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