Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation

TL;DR

This paper establishes new Gagliardo-Nirenberg interpolation inequalities that relate Sobolev semi-norms, including fractional orders, to bounded mean oscillation semi-norms, advancing the understanding of function space relationships.

Contribution

It introduces novel interpolation inequalities involving fractional Sobolev semi-norms and bounded mean oscillation, extending classical results to fractional orders.

Findings

Proved inequalities relating fractional Sobolev semi-norms and BMO semi-norms.

Extended classical Gagliardo-Nirenberg inequalities to fractional orders.

Provided new tools for analyzing function spaces with fractional smoothness.

Abstract

We prove Gagliardo-Nirenberg interpolation inequalities estimating the Sobolev semi-norm in terms of the bounded mean oscillation semi-norm and a Sobolev semi-norm, with some of the Sobolev semi-norms having fractional order.