Boundedness of generalized Riesz potentials on the variable Hardy spaces

TL;DR

This paper investigates the boundedness properties of generalized Riesz potentials on variable Hardy spaces, establishing conditions for their boundedness from Hp(.) to Lq(.) and within Hp(.)-Hq(.).

Contribution

It introduces new boundedness results for generalized Riesz potentials on variable Hardy spaces using finite atomic decomposition techniques.

Findings

Boundedness from Hp(.) to Lq(.) established

Hp(.)-Hq(.) boundedness proved

Utilizes finite atomic decomposition method

Abstract

We study the boundedness from Hp(.) into Lq(.) of certain generalized Riesz potentials and the Hp(.)-Hq(.) boundedness of the Riesz potential. Both results are achieved via the finite atomic decomposition developed in [4].