BMO: Oscillations, self improvement, Gagliardo coordinate spaces and reverse Hardy inequalities

TL;DR

This paper introduces coordinate Gagliardo spaces and a generalized John-Nirenberg Lemma to advance the understanding of BMO functions, providing new methods and applications for classical self-improving results.

Contribution

It presents a novel approach using coordinate Gagliardo spaces and extends the John-Nirenberg Lemma for BMO functions, offering new insights and tools.

Findings

Introduction of coordinate Gagliardo spaces

Generalized John-Nirenberg Lemma proved

Applications to classical self-improving results

Abstract

A new approach to classical self improving results for $BMO$ functions is presented. "Coordinate Gagliardo spaces" are introduced and a generalized version of the John-Nirenberg Lemma is proved. Applications are provided.