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arXiv · 2104.09826

Bochner-Riesz means for the Hermite and special Hermite expansions

Sanghyuk Lee·Jaehyeon Ryu
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Abstract

We consider the Bochner-Riesz means for the Hermite and special Hermite expansions and study their $L^p$ boundedness with the sharp summability index in a local setting. In two dimensions we establish the boundedness on the optimal range of $p$ and extend the previously known range in higher dimensions. Furthermore, we prove a new lower bound on the $L^p$ summability index for the Hermite Bochner-Riesz means in $\mathbb R^d$, $d\ge 2.$ This invalidates the conventional conjecture which was expected to be true.

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Sanghyuk Lee, Jaehyeon Ryu. 2021-04-20. Bochner-Riesz means for the Hermite and special Hermite expansions. https://arxiv.org/abs/2104.09826

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