Fractional type integral operators on variable Hardy spaces

TL;DR

This paper investigates the boundedness properties of fractional integral operators on variable Hardy spaces, establishing conditions under which these operators map between different function spaces.

Contribution

It provides new results on the boundedness of fractional integral operators and Riesz potentials on variable Hardy spaces, extending classical theory to variable exponent settings.

Findings

Fractional integral operators are bounded from Hp(.) to Lq(.)

Riesz potential is bounded from Hp(.) to Hq(.)

Conditions for boundedness depend on variable exponents

Abstract

We study the boundedness of certain fractional integral operators from Hp(.) into Lq(.). We also obtain the Hp(.)- Hq(.) boundedness of the Riesz potential.