Abstract framework for John Nirenberg inequalities and applications to Hardy spaces

TL;DR

This paper develops an abstract framework for John-Nirenberg inequalities related to BMO-type spaces, enabling the recovery of known inequalities and applications to atomic Hardy spaces.

Contribution

It introduces a general abstract framework for John-Nirenberg inequalities that unifies and extends previous results in Hardy space theory.

Findings

Recovered several known John-Nirenberg inequalities

Provided new applications to atomic Hardy spaces

Extended the theoretical understanding of BMO-type spaces

Abstract

In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy spaces. Moreover, we show that our assumptions allow us to recover some already known John-Nirenberg inequalities. We give applications to the atomic Hardy spaces too.