Real Interpolation method, Lorentz spaces and refined Sobolev inequalities

TL;DR

This paper provides a straightforward proof of refined inequalities between Lorentz and Besov spaces, generalizing previous results and analyzing their sharpness and optimality using real interpolation space characterization.

Contribution

It introduces a new, simplified proof of refined Lorentz-Besov inequalities and extends prior work by Bahouri and Cohen with a focus on sharpness and optimality.

Findings

Established refined inequalities between Lorentz and Besov spaces

Generalized previous results of Bahouri and Cohen

Analyzed the sharpness and optimality of these inequalities

Abstract

In this article we give a straightforward proof of refined inequalities between Lorentz spaces and Besov spaces and we generalize previous results of H. Bahouri and A. Cohen. Our approach is based in the characterization of Lorentz spaces as real interpolation spaces. We will also study the sharpness and optimality of these inequalities.