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arXiv · 2501.08832

Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes

Guixiang Hong·Xudong Lai·Liang Wang
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Abstract

In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to Mockenhaupt$-$Seeger$-$Sogge \cite{MSS}. As an application and simultaneously one motivation, we obtain the noncommutative analogue of Bourgain's circular maximal theorem, resolving one problem after \cite{Hong}.

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Guixiang Hong, Xudong Lai, Liang Wang. 2025-01-15. Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes. https://arxiv.org/abs/2501.08832

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