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arXiv · 2203.09058

On the $L^2$ boundedness of pseudo-multipliers for Hermite expansions

Fu Ken Ly
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Abstract

We give various conditions for Hermite pseudo-multipliers to be bounded on $L^2(\mathbb{R}^n)$. As a by-product we also give results on $L^p(\mathbb{R}^n)$, as well as new results for pseudo-multipliers for the Gaussian measure setting. One of our key tools is a new integration by-parts formula for Hermite expansions.

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Fu Ken Ly. 2022-03-17. On the $L^2$ boundedness of pseudo-multipliers for Hermite expansions. https://arxiv.org/abs/2203.09058

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