非齐度量测度空间上Morrey-Herz空间上的Calderon-Zygmund算子及其交换子

Calderon-Zygmund Operators and Commutators on Morrey-Herz Spaces with Non-Homogeneous Metric Measure

设(X,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,本文中,引进一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,特别是η-弱逆倍条件,证明Calderon-Zygmund算子及其交换子在Morrey-Herz空间上的有界性.

Let(X,d,μ)be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling conditions.In this paper,the Morrey-Herz spaces on the non-homogeneous metric measure space are introduced.Then,by the properties of the non-homogeneous metric measure space,in particular theη-weak reverse doubling condition,the boundedness of Calderon-Zygmund operators and their commutators on the Morrey-Herz spaces with non-homogeneous metric measure is obtained.