Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes
Functional Analysis
2025-03-13 v2
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 MockenhauptSeegerSogge \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}.
Keywords
Cite
@article{arxiv.2501.08832,
title = {Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes},
author = {Guixiang Hong and Xudong Lai and Liang Wang},
journal= {arXiv preprint arXiv:2501.08832},
year = {2025}
}
Comments
41 pages,change in the title