Bochner-Riesz means for the Hermite and special Hermite expansions

2021/04/20 by Sanghyuk Lee, Lee, Sanghyuk, Jaehyeon Ryu +1 · 3 citations
Mathematics · #42B99 #42C10 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2104.09826

openalex publication_date 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 2. This invalidates the conventional conjecture which was expected to be true.

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