Gagliardo-Nirenberg type inequalities with a BMO term and fractional Laplacians

TL;DR

This paper improves a global Gagliardo-Nirenberg inequality by incorporating fractional Laplacians and BMO terms, also providing local versions for broader applicability.

Contribution

It introduces an enhanced inequality involving fractional Laplacians and BMO terms, extending previous results to a more general setting.

Findings

Established a global Gagliardo-Nirenberg inequality with BMO and fractional Laplacians.

Provided local versions of the inequality.

Extended the inequality to include fractional derivatives.

Abstract

An improvement of a {\em Global (strong) Gagliardo-Nienberg inequality with a BMO term} is established by replacing local derivatives by {\em and fractional Laplacians.} Local versions are also given.