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arXiv · 2407.20887

On almost everywhere convergence of planar Bochner-Riesz means

Xiaochun Li·Shukun Wu
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Abstract

We demonstrate the almost everywhere convergence of the planar Bochner-Riesz means for $L^p$ functions in the optimal range when $5/3\leq p\leq 2$. 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 $L^2$ estimate, which may be of independent interest.

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Xiaochun Li, Shukun Wu. 2024-07-30. On almost everywhere convergence of planar Bochner-Riesz means. https://arxiv.org/abs/2407.20887

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