Limit case of Hardy-Littlewood-Sobolev inequality for martingales

TL;DR

This paper extends the Stein-Weiss inequality to the setting of arbitrary martingales, broadening the scope of classical harmonic analysis results to stochastic processes.

Contribution

It introduces a martingale version of the Hardy-Littlewood-Sobolev inequality, generalizing existing inequalities to a new probabilistic context.

Findings

Established a Stein-Weiss inequality for martingales.

Demonstrated the inequality's applicability to various martingale types.

Provided theoretical foundations for future stochastic analysis applications.

Abstract

We provide a version of the Stein-Weiss inequality for arbitrary martingales.