度量测度空间上θ型Marcinkiewicz积分及交换子  

θType Marcinkiewicz Integral and Its Commutator on Metric Measure Spaces

作　　者：逯光辉 陶双平 Lu Guanghui;Tao Shuangping(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学物理学报（A辑）》2020年第6期1431-1445,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561062);甘肃省高等学校科研项目(2020A-010);西北师范大学青年教师科研能力项目(NWNU-LKQN2020-07);西北师范大学博士启动基金(0002020203)。

摘　　要：设(χ,d,μ)是Hytönen意义下的非齐度量测度空间且满足所谓的几何双倍和上部双倍条件.在假设控制函数λ满足κ-弱逆双倍条件下,该文主要证明了θ型Marcinkiewicz积分Mθ及由具有离散系数的平均振荡空间RBMO(μ)与Mθ生成的交换子Mθ,b在齐次Herz空间Kq^τ,p(μ)上的有界性,也得到了Mθ与Mθ,b从HKatb,q^τp(μ)到Kq^τ,p(μ)上的有界性.Let(X,d,μ)be a non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions in the sense of Hytonen.Under the assumption that the dominating function A satisfies the e-weak reverse doubling condition,the authors prove that theθtype Macinkiewicz integral Mθand the commutator Mθ,b generated by the b∈RBMO(μ)and the Mθis bounded on homogeneous Herz space Kq^τ,p(μ),respectively.Furthermore,the boundeness of the Mθand Mθ,b from the HKatb,q^τ,p(μ)into the Kq^τ,p(μ)is also obtained.

关 键 词：非齐度量测度空间 θ型Marcinkiewicz积分 交换子 LIPSCHITZ函数 HERZ空间 原子Herz-Hardy空间 

分 类 号：O174.2[理学—数学]