Weighted Variation Inequalities for Singular Integrals and Commutators in Rearrangement Invariant Banach and Quasi-Banach Spaces  

作　　者：Jia Wei TAN Qing Ying XUE 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China

出　　处：《Acta Mathematica Sinica,English Series》2023年第7期1389-1413,共25页数学学报（英文版）

基　　金：supported partly by the National Key R&D Program of China (Grant No.2020YFA0712900);NNSF of China (Grant Nos. 11871101, 12271041)。

摘　　要：In order to study the boundedness of some operators in general function spaces which include Lorentz spaces and Orlicz spaces as special examples,Lorentz introduced a new space called rearrangement invariant Banach function spaces,denoted by RIBFS.It is shown in this paper that variation operators of singular integrals and their commutators are bounded on RIBFS whenever the kernels satisfy the L~r-H?rmander conditions.Moreover,we obtain some quantitative weighted bounds in the quasi-Banach spaces and modular inequalities for above variation operators and their commutators.

关 键 词：Variation operators singular integrals COMMUTATORS sparse operators rearrangement invariant Banach function spaces 

分 类 号：O177[理学—数学]