A thin-thick Decomposition for Hardy Martingales

TL;DR

This paper introduces a thin-thick decomposition for Hardy martingales, enhancing their square function characterization and providing new proofs for classical martingale inequalities.

Contribution

It presents a novel thin-thick decomposition method for Hardy martingales and strengthens their square function characterization.

Findings

Established a thin-thick decomposition for Hardy martingales

Strengthened the square function characterization of Hardy martingales

Provided new proofs for classical martingale inequalities

Abstract

We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classical martingale inequalities, for which we give new proofs .