Characterization of Lipschitz Functions via Commutators of Multilinear Singular Integral Operators in Variable Lebesgue Spaces

作     者：Jiang Long WU Pu ZHANG Jiang Long WU;Pu ZHANG

作者机构：Department of MathematicsMudanjiang Normal UniversityMudanjiang 157011P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第12期

页      面：2465-2488页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571160) the Research Funds for the Educational Committee of Heilongjiang(Grant No.2019-KYYWF-0909) the Reform and Development Foundation for Local Colleges and Universities of the Central Government(Grant No.2020YQ07) 

主　　题：Multilinear commutator singular integral operator Lipschitz function variable exponent 

摘      要：Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator *** by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,*** main purpose of this paper is to establish some new characterizations of the(variable)Lipschitz spaces in terms of the boundedness of multilinear commutator T∑b in the context of the variable exponent Lebesgue spaces,that is,the authors give the necessary and sufficient conditions for bj(j=1,2,...,m)to be L(δ)or L(δ(·))via the boundedness of multilinear commutator from products of variable exponent Lebesgue spaces to variable exponent Lebesgue *** authors do so by applying the Fourier series technique and some pointwise esti-mate for the *** key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.