Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes
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 MSS. As an application and simultaneously one motivation, we obtain the noncommutative analogue of Bourgain's circular maximal theorem, resolving one problem after Hong.
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