BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT

Title & Authors
BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT
Wu, Jianglong;

Abstract
In this paper, the fractional Hardy-type operator of variable order $\small{{\beta}(x)}$ is shown to be bounded from the Herz-Morrey spaces $\small{M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)}$ with variable exponent $\small{q_1(x)}$ into the weighted space $\small{M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})}$, where $\small{{\omega}=(1+|x|)^{-{\gamma}(x)}}$ with some $\small{{\gamma}(x)}$ > 0 and $\small{1/q_1(x)-1/q_2(x)={\beta}(x)/n}$ when $\small{q_1(x)}$ is not necessarily constant at infinity. It is assumed that the exponent $\small{q_1(x)}$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $\small{q_1({\infty}){\leq}q_1(x){\leq}(q_1)+}$ < $\small{{\infty}(x{\in}\mathbb{R}^n)}$.
Keywords
Herz-Morrey space;Hardy operator;Riesz potential;variable exponent;weighted estimate;
Language
English
Cited by
1.
Boundedness for Higher Order Commutators of Fractional Integrals on Variable Exponent Herz–Morrey Spaces, Mediterranean Journal of Mathematics, 2017, 14, 5
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