Weighted estimates for bilinear square functions with non-smooth kernels and commutators  

作　　者：Rui BU Zunwei FU Yandan ZHANG 

机构地区：[1]Department of Mathematics,Qingdao University of Science and Technology,Qingdao 266061,China [2]School of Mathematics and Statistics,Linyi University,Linyi 276005,China [3]School of Mathematical Sciences,Qufu Normal University,Qufu 273100,China

出　　处：《Frontiers of Mathematics in China》2020年第1期1-20,共20页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11671185,11571306,11671363,11771195);the Natural Science Foundation of Shandong Province(Grant Nos.ZR2018PA004,ZR2016AB07,ZR2018LA002,ZR2019YQ04).

摘　　要：Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions.

关 键 词：BILINEAR square FUNCTION NON-SMOOTH kernel weight COMMUTATOR BMO FUNCTION 

分 类 号：O17[理学—数学]