Gagliardo-Nirenberg Inequalities in Fractional Coulomb-Sobolev spaces for Radial functions

TL;DR

This paper extends the parameter range for Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces specifically for radial functions and investigates the optimality of these new ranges.

Contribution

It introduces an extended parameter range for inequalities in fractional Coulomb-Sobolev spaces and analyzes their optimality for radial functions.

Findings

Extended the parameter range for inequalities in fractional Coulomb-Sobolev spaces.

Proved the optimality of the extended parameter range.

Focused on radial functions in the analysis.

Abstract

We extend the range of parameters associated with the Gagliardo-Nirenberg interpolation inequalities in the fractional Coulomb-Sobolev spaces for radial functions. We also study the optimality of this newly extended range of parameters.