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

作　　者：Jiang Long WU Pu ZHANG 

机构地区：[1]Department of Mathematics,Mudanjiang Normal University,Mudanjiang 157011,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第12期2465-2488,共24页数学学报（英文版）

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)。

摘　　要：Let 6=(bi,b2,...,bm)be a collection of locally integrable functions and T,the com-mutator of multilinear singular integral operator T.Denote by L(δ)and L(δ(·))the Lipschitz spaces and the variable Lipschitz spaces,respectively.The 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 spaces.The authors do so by applying the Fourier series technique and some pointwise esti-mate for the commutators.The key tool in obtaining such pointwise estimate is a certain generalization of the classical sharp maximal operator.

关 键 词：Multilinear commutator singular integral operator Lipschitz function variable exponent 

分 类 号：O177[理学—数学]