报告题目： Problems relatedto pointwise convergence for Schrodinger groups

报告时间：2025年1月6日  （周一）10：00  

报告地点：综合楼644会议室

报告人：邓清泉

报告人简介：

邓清泉，华中师范大学副教授、博士生导师。主要从事调和分析Hardy空间理论、高阶薛定谔算子热核估计以及非线性薛定谔方程孤立波动力性质等研究，在 Adv.Math.，Comm. Math.Phys.，J. Funct. Anal.，Indiana Univ. Math. J. 以及 SIAM J. Math. Anal.等SCI期刊上发表多篇论文。先后主持博士后基金、国家自然科学基金青年项目与面上项目、湖北省自然科学基金等。

报告摘要：

 In this work, we focus on the maximalestimates and pointwise convergence for Schrodinger group $e^{itH}$ withpotentials in dimension one, where $H=-/Delta+V$. Under some assumptions onpotential V, by using the distorted Fourier transform, as well as the functionspaces associated to operators, we prove the boundedness for different types ofmaximal operators related to $e^{itH}$, which will be used to studied thepointwise convergence, the rete for pointwise convergence and the convergencealong curves for e^{itH}. We also show that the exponents showed up in maximalinequalities and pointwise convergence are optimal. Moreover, we also considerthe Hausdorff dimensions for the divergence sets.