论平面 Bochner-Riesz 平均值的几乎无处收敛性

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-30 DOI:arxiv-2407.20887

Xiaochun Li, Shukun Wu

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引用次数: 0

摘要

我们证明，当 $5/3\leqp\leq 2$ 时，L^p$ 函数的 PlanarBochner-Riesz means 几乎无处不收敛。这是通过为与波赫纳-里兹乘法算子密切相关的最大算子建立一个尖锐的$L^{5/3}$估计值来实现的。

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On almost everywhere convergence of planar Bochner-Riesz mean

We demonstrate that 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 novel refined $L^2$ estimate, which may be of independent interest.

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arXiv - MATH - Classical Analysis and ODEs

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