On weighted compactness of commutators of bilinear vector-valued singular integral operators and applications
作者机构：School of Mathematics & Computational Science Hunan University of Science and Technology School of Mathematics & Computational Science Xiangtan University School of Mathematical Sciences Laboratory of Mathematics and Complex Systems Ministry of Education Beijing Normal University
出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期：2024年
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：Z. Li was supported by the National Natural Science Foundation of China (Grant No. 12101222) Scientific Research Fund of Hunan Provincial Education Department (Grant No. 23B0458) F. Liao was supported by the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 22B0155) Q. Xue was partly supported by the National Key R&D Program of China (Grant No. 2020YFA0712900) National Natural Science Foundation of China (Grant No. 12271041)
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 Calderón-Zygmund *** any b=(b1,b2) ∈(CMO(Rn))2,let [T,bj]ej(j=1,2),[T,■]_α be the commutators in the j-th entry and the iterated commutators of T,*** this paper,for all p0 1,p0/2 p ∞,and p0≤p1,p2∞ with 1/p=1/p1+ 1/p2,we prove that(T,bj]ejand [T,b]_α are weighted compact operators from Lp1(w1) × Lp2,(w2) to Lp(v_■),where ■=(w1,w2) ∈A■/p0and v_■=w1p/p1w2p/*** applications,we obtained 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 g_λ~* 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 g_λ~* function and bilinear Lusin’s area integral,respectively.
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