Abstract
Abstract We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.
Highlights
This paper focuses on the Hardy’s inequalities and the boundedness of the integral operators on Herz-Morrey spaces.Herz-Morrey spaces are extensions of Herz spaces [1] and Morrey spaces [2]
We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces
These results give us the Hardy’s inequalities and the mapping properties of the integral operators on HerzMorrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces
Summary
This paper focuses on the Hardy’s inequalities and the boundedness of the integral operators on Herz-Morrey spaces. We study the mapping properties of integral operators on Herz-Morrey spaces. We give some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. With these estimates, we de ne and obtain the Boyd indices of Herz-Morrey spaces. We de ne and obtain the Boyd indices of Herz-Morrey spaces By using these indices, we establish the a general result on the mapping properties of integral operators on Herz-Morrey spaces. We establish the a general result on the mapping properties of integral operators on Herz-Morrey spaces This general result yields the boundedness of Hadamard fractional integrals, the
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