Title: Almost everywhere convergence of Bochner-Riesz means for the Hermite operator
Speaker: Lixin Yan (Zhongshan University)
Time: 16:00-17:30, July3
Location: Tecent Meeting, Tecent Meeting ID: 352 563 564
Abstract: In this talk I will discuss almost everywhere convergence of Bochner-Riesz means for the Hermite operator $H = -\Delta + |x|^2$. We prove that $ $ \lim\limits_{R\to \infty} S_R^{\lambda}(H) f(x)=f(x) \ \text{a.e.}$ $ for $f\in L^p(\mathbb R^n)$ provided that $p\geq 2$ and $ \lambda> 2^{-1}\max\big\{ n\big({1/2}-{1/p}\big)-{1/ 2}, \, 0\big\}.$ Surprisingly, for the dimensions $n\geq 2$ our result reduces the borderline summability index $\lambda$ for a.e. convergence as small as only half of the critical index required for a.e. convergence of the classical Bochner-Riesz means for the Laplacian. This is a joint work with Peng Chen, Xuan Thinh Duong, Danqing He and Sanghyuk Lee.
Meeting Link：https://meeting.tencent.com/s/vORFGj8FpYMP
