广义分数次积分算子及其交换子在非齐型度量测度空间上的有界性

Boundedness of Generalized Fractional Integral Operators and Their Commutators on Non-homogeneous Metric Measure Spaces

设(X,d,μ)是一个满足上双倍条件和几何双倍条件的非齐型度量测度空间.本文利用非齐型度量测度空间的性质和不等式技巧,借助于广义分数次积分算子在L^(p)空间上的有界性理论,证明了广义分数次积分算子及其交换子在非齐型度量测度Morrey-Herz空间上的有界性.

Let(X,d,u)be a non-homogeneous metric measure space,satisfying both the geometrical doubling and the upper doubling conditions.In this paper,by using the properties of non-homogeneous metric measure space and inequality technique,applying the theory of boundedness for generalized fractional integral operators on the L^(p)spaces,the authors proved that the generalized fractional integral operators and their commutators are bounded on MorreyHerz spaces with non-homogeneous metric measure.