English

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 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}.

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