Mixed Sobolev-like Inequalities in Lebesgue spaces of variable exponents and in Orlicz spaces

TL;DR

This paper presents a version of Hedberg's inequality that simplifies deriving functional inequalities for Sobolev and Besov spaces within Lebesgue spaces of variable exponents and Orlicz spaces.

Contribution

It introduces a new version of Hedberg's inequality applicable to variable exponent Lebesgue spaces and Orlicz spaces, facilitating easier derivation of functional inequalities.

Findings

Simplified derivation of Sobolev and Besov inequalities

Applicable to variable exponent Lebesgue spaces

Extends to Orlicz space framework

Abstract

In this short article we show a particular version of the Hedberg inequality which can be used to derive, in a very simple manner, functional inequalities involving Sobolev and Besov spaces in the general setting of Lebesgue spaces of variable exponents and in the framework of Orlicz spaces.