On Weighted Compactness of Commutators of Bilinear Vector-valued Singular Integral Operators and Applications

作     者：Zhengyang Li Liu Lu Fanghui Liao Qingying Xue Zhengyang Li;Liu Lu;Fanghui Liao;Qingying Xue

作者机构：School of Mathematics&Computational ScienceHu’nan University of Science and TechnologyXiangtan 411201P.R.China School of Mathematics&Computational ScienceXiangtan UniversityXiangtan 411105P.R.China School of Mathematical SciencesLaboratory of Mathematics and Complex Systems Ministry of EducationBeijing Normal UniversityBeijing 100875P.R.China 

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

年 卷 期：2025年第41卷第1期

页      面：169-190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.12101222) National Natural Science Foundation of China(Grant No.12271041) Scientific Research Fund of Hunan Provincial Education Department(Grant No.23B0458) supported by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0155) partly supported by the National Key R&D Program of China(Grant No.2020YFA0712900) 

主　　题：Weighted compactness commutators multilinear square functions Fourier multiplier operator 

摘      要：Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions,which may not fall under the scope of the theory of standard Calder¬on–Zygmund *** anyb^(→)=(b_(1),b_(2))∈(CMO(R^(n)))^(2),let[T,b_(j)]e_(j)(j=1,2),[T,→b]_(α)be the commutators in the j-th entry and the iterated commutators of T,*** this paper,for all p_(0)1,p0/2p∞,and p0≤p1,p2∞with 1/p=1/p1+1/p2,we prove that[T,b_(j)]_(ej) and[T,b^(→)]αare weighted compact operators from L^(p1)(w1)×L^(p2)(w2)to L^(p)(νw^(→)),wherew^(→)=(w1,w2)∈A_(p^(→)/p0) andνw^(→)=w_(1)^(p/p1) w_()2)^(p/p2).As applications,we obtain the weighted compactness of commutators in the j-th entry and the iterated commutators of several kinds of bilinear Littlewood–Paley square operators with some mild kernel regularity,including bilinear g function,bilinear gλ^(∗)function and bilinear Lusin’s area *** addition,we also get the weighted compactness of commutators in the j-th entry and the iterated commutators of bilinear Fourier multiplier operators,and bilinear square Fourier multiplier operators associated with bilinear g function,bilinear gλ^(∗) function and bilinear Lusin’s area integral,respectively.