Bilinear Strongly Singular Calderón-Zygmund Operators and Their Commutators on Non-Homogeneous Generalized Morrey Spaces  

作　　者：Guanghui LU Miaomiao WANG 

机构地区：[1]College of Mathematics and Statistics,Northwest Normal University,Gansu 730070,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第1期43-62,共20页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12201500);the Science Foundation for Youths of Gansu Province(Grant No.22JR5RA173);the Young Teachers’Scientific Research Ability Promotion Project of Northwest Normal University(Grant No.NWNU-LKQN2020-07)。

摘　　要：The main goal of this paper is to establish the boundedness of bilinear strongly singular operator T^(-)and its commutator Tb_(1),b_(2)on generalized Morrey spaces M_(p)^(u)(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to W_(τ)forτ∈(0,2),and u1u2=u.The authors prove that T_(-)is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ),where 1/p=1/p_(1)+1/p_(2)with 1<p1,p2<∞;and also bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into generalized weak Morrey spaces WM_(p)^(u)(μ).Furthermore,the author also show that commutator Tb1,b2 generated by b_(1),b_(2)∈RBMO(μ)and T is bounded from product spaces M_(p1)^(u1)(μ)×M_(p2)^(u2)(μ)into spaces M_(p)^(u)(μ).

关 键 词：non-homogeneous metric measure space bilinear strongly singular Calder´on-Zygmund operator commutator space~RBMO(μ) generalized Morrey space 

分 类 号：O177[理学—数学]