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arXiv · 2304.04373

Weighted 1-dimensional Orlicz-Poincaré inequalities

Lyudmila Korobenko·Olly Milshstein·Lucas Yong
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Abstract

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 $q > p$.

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Lyudmila Korobenko, Olly Milshstein, Lucas Yong. 2023-06-28. Weighted 1-dimensional Orlicz-Poincaré inequalities. https://doi.org/10.1016/j.jmaa.2023.127649

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