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 颜立新—— Almost everywhere convergence of Bochner-Riesz means for the Hermite operators
 发布人：许全华  发布时间：2020-06-29   浏览次数:549
 标题：Almost everywhere convergence of Bochner-Riesz means for the Hermite operator报告人：颜立新（中山大学数学系）时间：7月3日，16:00-17:30地点：腾讯会议，会议 ID：352 563 564摘要：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.