On almost everywhere convergence of planar Bochner-Riesz means

2024/07/30 by Xiaochun Li, Shukun Wu, Li, Xiaochun +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2407.20887

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate the almost everywhere convergence of the planar Bochner-Riesz means for L^p functions in the optimal range when 5/3≤ p≤ 2. This is achieved by establishing a sharp L^5/3 estimate for a maximal operator closely associated with the Bochner-Riesz multiplier operator. The estimate depends on a new refined L² estimate, which may be of independent interest.

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