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

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

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The main goal of this paper is to establish the boundedness of bilinear strongly singular operator (T) and its commutator (T)b1,b2 on generalized Morrey spaces Mup(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to Wτ for τ ∈(0,2),and u1u2=u.The authors prove that (T) is bounded from product spaces Mu1p1(μ×Mu2p2(μ)into spaces Mup(μ),where 1/p=1/p1+1/p2 with 1＜p1,p2＜∞;and also bounded from product spaces Mu1p1(μ)×Mu2p2(μ)into generalized weak Morrey spaces WMup(μ).Furthermore,the author also show that commutator (T)b1,b2generated by b1,b2 ∈RBMO(μ)and (T) is bounded from product spaces Mu1p1(μ)× Mu2p2(μ)into spaces Mup(μ).

non-homogeneous metric measure spacebilinear strongly singular Calderón-Zygmund operatorcommutatorspace RBMO(μ)generalized Morrey space

Guanghui LU、Miaomiao WANG

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College of Mathematics and Statistics,Northwest Normal University,Gansu 730070,P.R.China

国家自然科学基金Science Foundation for Youths of Gansu ProvinceYoung Teachers'Scientific Research Ability Promotion Project of Northwest Normal University

1220150022JR5RA173NWNU-LKQN2O20-07

2024

10.3770/j.issn:2095-2651.2024.01.006

数学研究及应用
大连理工大学

数学研究及应用

影响因子：0.094
ISSN：2095-2651
年,卷(期)：2024.44(1)
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