Analysis & Applications Seminar
Endpoint estimates and local smoothing for the fractal spherical maximal function
Speaker: Luz Roncal (BCAM)Date: Friday, 17 April 2026 - 11:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
The spherical maximal function is a fundamental object in harmonic analysis, closely connected to solutions of the wave equation and their associated smoothing properties. Variants of this operator have been extensively studied in the literature. More recently, there has been growing interest in establishing sharp Lp − Lq bounds when the supremum is taken over dilation sets of fractal nature.
In this talk, we present missing endpoint estimates for the fractal spherical maximal function which were open when d = 2. We also investigate closely related Lp −Lq local smoothing estimates for the wave operator over fractal dilation sets. Our approach is based on bilinear restriction estimates for the cone, building on influential work by T. Wolff and T. Tao.
This is joint work with Sanghyuk Lee, Feng Zhang, and Shuijiang Zhao.
