分析和微分方程讨论班

报告题目：Spherical maximal operators on radial functions

报告人：赵水江（首尔国立大学） 

时间：2026年8月1日，10:20-11:20

地点：海纳苑2幢312

摘要：We study the spherical maximal operator  over a fractal set $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p$-improving estimates. In two dimensions, sharp results are also obtained for quasi-Assouad regular sets $E$. A notable feature is that the high-dimensional results depend solely on the upper Minkowski dimension, while the two-dimensional results also involve other concepts in fractal geometry such as the upper Assouad spectrum. Additionally, the geometric shapes of the regions corresponding to the sharp $ L^p$-improving bounds differ significantly between the two cases.

联系人：王梦（mathdreamcn@zju.edu.cn）