【分析和微分方程讨论班】Endpoint estimates for the fractal circular maximal function and related local smoothing

Speaker：赵水江（Postdoctoral researcher,  Seoul National University）

Time：2026年2月6日（星期五），上午10:30-11:30

Place：海纳苑2幢1120

Abstract: Sharp $L^p$--$L^q$ estimates for  the  spherical maximal function  over dilation sets of fractal dimensions, including the endpoint estimates, were recently  proved  by Anderson--Hughes--Roos--Seeger. More intricate $L^p$--$L^q$ estimates for the fractal circular maximal function were later established  in the sharp range by  Roos--Seeger, but the endpoint estimates have been left open, particularly when the fractal dimension of the dilation set  lies in $[1/2, 1)$.  In this work, we prove these  missing  endpoint estimates for the circular maximal function. We also study  the closely  related   $L^p$--$L^q$ local smoothing estimates for the wave operator over fractal dilation sets. Making use of a bilinear approach, we also extend the range of $p,q$, for which  the optimal estimate holds. This is a joint work with Sanghyuk Lee, Luz Roncal and Feng Zhang.

Contact Person: 王梦(mathdreamcn@zju.edu.cn)