Gagliardo-Nirenberg type inequalities using fractional Sobolev spaces and Besov spaces

TL;DR

This paper develops Gagliardo-Nirenberg inequalities within fractional Sobolev and Besov spaces, extending previous results to broader fractional function spaces for advanced analysis.

Contribution

It introduces new Gagliardo-Nirenberg inequalities involving fractional homogeneous Sobolev and Besov spaces, expanding the theoretical framework.

Findings

Extended Gagliardo-Nirenberg inequalities to fractional spaces

Generalized previous results in fractional Sobolev and Besov contexts

Provided new tools for analysis in fractional function spaces

Abstract

Our main purpose is to establish Gagliardo-Nirenberg type inequalities using fractional homogeneous Sobolev spaces, and homogeneous Besov spaces. In particular, we extend some of the results obtained by the authors in [1, 2, 3, 7, 16, 21].