On the \(L^2\) boundedness of pseudo-multipliers for Hermite expansions

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...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Author: Fu, Ken Ly
Format: Article
Language:English
Subjects:
Multipliers
Online Access:Get full text
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Summary: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.
ISSN:2331-8422