Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on quantum Euclidean space

Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on quantum Euclidean space

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...

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Hauptverfasser: Hong, Guixiang, Lai, Xudong, Wang, Liang
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Functional Analysis
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Zusammenfassung: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}.
DOI:10.48550/arxiv.2501.08832