Almost everywhere convergence of Bochner--Riesz means for the twisted Laplacian

2023/03/05 by Eun-Hee Jeong, Sanghyuk Lee, Jeong, Eunhee +3 · 1 citation
Mathematics · #42B15 #42B25 #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.2303.02679

openalex publication_date 2023/03/05 · openalex created_date 2023/03/09 · openalex updated_date 2026/07/28

Abstract

Let \mathcal L denote the twisted Laplacian in \mathbb C^d. We study almost everywhere convergence of the Bochner--Riesz mean S^δ_t(\mathcal L) f of f∈ L^p(\mathbb C^d) as t→ ∞, which is an expansion of f in the special Hermite functions. For 2≤ p≤ ∞, we obtain the sharp range of the summability indices δ for which the convergence of S^δ_t(\mathcal L) f holds for all f∈ L^p(\mathbb C^d).

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