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arXiv · 2111.10619

Hardy's inequality for Hermite expansions revisited

Peng Chen·Jinsen Xiao
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Abstract

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators. When the space dimension is $1$, we obtain a new estimate of Hardy's inequality for Hermite expansions in $H^p({\mathbb R})$ for the range $0<p<1.$

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Peng Chen, Jinsen Xiao. 2021-11-20. Hardy's inequality for Hermite expansions revisited. https://arxiv.org/abs/2111.10619

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