Weighted Orlicz-Poincar\'e inequalities in product spaces

TL;DR

This paper extends the theory of weighted Orlicz-Poincaré inequalities to product spaces, providing necessary and sufficient conditions, building on prior work for weighted Poincaré inequalities.

Contribution

It introduces new criteria for weighted Orlicz-Poincaré inequalities in product spaces, advancing the understanding of functional inequalities in complex spaces.

Findings

Established necessary and sufficient conditions for these inequalities

Extended previous results from weighted Poincaré to Orlicz-Poincaré inequalities

Built upon the work of Chua and Wheeden

Abstract

This article is a follow-up to arXiv:2304.04373. We establish necessary and sufficient conditions for weighted Orlicz-Poincar\'e inequalities in product spaces. These results follow the work of Chua and Wheeden, who established similar results for weighted Poincar\'e inequalities in product spaces.