Inequalities for convolutions of functions on commutative hypergroups

TL;DR

This paper extends the Young inequality to Lorentz spaces on commutative hypergroups and applies it to establish boundedness and Hardy-Littlewood-Sobolev type results for fractional integrals in this setting.

Contribution

It introduces a generalized Young inequality for Lorentz spaces on commutative hypergroups and proves related boundedness and integral theorems.

Findings

Established the generalized Young inequality on Lorentz spaces for commutative hypergroups.

Proved boundedness of fractional integrals on Lorentz spaces.

Extended Hardy-Littlewood-Sobolev theorem to the hypergroup setting.

Abstract

The generalized Young inequality on the Lorentz spaces for commutative hypergroups is introdused and an application of it is given to the theory of fractional integrals. The boundedness on the Lorentz space and the Hardy-Littlewood-Sobolev theorem for the fractional integrals on the commutative hypergroups is proved.