Commutators, paraproducts and BMO in non-homogeneous martingale settings

TL;DR

This paper explores the relationships between BMO spaces, paraproducts, and commutators within non-homogeneous martingale frameworks, presenting new findings and alternative proofs to existing results.

Contribution

It introduces novel results linking BMO, paraproducts, and commutators in non-homogeneous martingale settings, expanding understanding in this area.

Findings

New relationships between BMO spaces and paraproducts

Unexpected results in non-homogeneous martingale contexts

Alternative proofs of known theorems

Abstract

In this paper we investigate the relations between (martingale) BMO spaces, paraproducts and commutators in non-homogeneous martingale settings. Some new, and one might add unexpected, results are obtained. Some alternative proof of known results are also presented.