Problems related to pointwise convergence for Schrodinger groups

Speaker:  邓清泉（华中师范大学）

Time:  2025-01-07，10:20-11:20

Location: 海纳苑2幢205

Abstract: In this work, we focus on the maximal estimates and pointwise convergence for Schrodinger group $e^{itH}$ with potentials in dimension one, where $H=-\Delta+V$. Under some assumptions on potential V, by using the distorted Fourier transform, as well as the function spaces associated to operators, we prove the boundedness for different types of maximal operators related to $e^{itH}$, which will be used to studied the pointwise convergence, the rete for pointwise convergence and the convergence along curves for e^{itH}. We also show that the exponents showed up in maximal inequalities and pointwise convergence are optimal. Moreover, we also consider the Hausdorff dimensions for the divergence sets.

Contact Person:  王梦(mathdreamcn@zju.edu.cn)