arXiv subjects
Publications and source records attributed to Lucas Yong.
This article is a follow-up to arXiv:2304.04373. We establish necessary and sufficient conditions for weighted Orlicz-Poincaré inequalities in product spaces. These results follow the work of Chua and Wheeden, who established similar results for weighted Poincaré inequalities in product spaces.
In this paper we establish necessary and sufficient conditions for weighted Orlicz-Poincaré inequalities in dimension one. Our theorems generalize the main results of Chua and Wheeden, who established necessary and sufficient conditions for weighted $(q,p)$ Poincaré inequalities. We give an example of a weight satisfying sufficient conditions for a $(Φ, p)$ Orlicz-Poincaré inequality where the gauge norm with respect to $Φ$ is a bump on the Lebesgue $L^p$ norm. This weight, on the other hand, does not satisfy a $(q,p)$ Poincaré inequality for any $q > p$.