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arXiv · 2309.03424

Calder\'on-Zygmund operators and endpoint spaces for Hermite expansions

The Anh Bui·Fu Ken Ly
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Abstract

Let $L=-\Delta +|x|^2$ be the Hermite operator on $\mathbb{R}^n$, and $T$ be a Calder\'on-Zygmund type operator that is modelled on certain singular integrals related to $L$. We establish necessary and sufficient conditions for $T$ to be bounded on various function spaces including the Hardy spaces and the Lipschitz spaces associated to $L$. We then apply our results to study the boundedness of the Riesz transforms and pseudo-multipliers associated to $L$.

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The Anh Bui, Fu Ken Ly. 2023-09-07. Calder\'on-Zygmund operators and endpoint spaces for Hermite expansions. https://arxiv.org/abs/2309.03424

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