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arXiv · 2405.02607

On pointwise convergence of cone multipliers

Peng Chen·Danqing He·Xiaochun Li·Lixin Yan
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Abstract

For $p\ge 2$, and $\lambda>\max\{n|\tfrac 1p-\tfrac 12|-\tfrac12, 0\}$, we prove the pointwise convergence of cone multipliers, i.e. $$ \lim_{t\to\infty}T_t^\lambda(f)\to f \text{ a.e.},$$ where $f\in L^p(\mathbb R^n)$ satisfies $supp\ \widehat f\subset\{\xi\in\mathbb R^n:\ 1<|\xi_n|<2\}$. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.

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Peng Chen, Danqing He, Xiaochun Li, Lixin Yan. 2024-05-04. On pointwise convergence of cone multipliers. https://arxiv.org/abs/2405.02607

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