On the $L^2$ boundedness of pseudo-multipliers for Hermite expansions
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- arXiv:
- arXiv:2203.09058
- Bibcode:
- 2022arXiv220309058L
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Functional Analysis;
- 42C15;
- 33C45;
- 35S05;
- 42B20
- E-Print:
- Some simplifications along with an updated section on Gaussian pseudo-multipliers