On convergence properties for generalized Schr\"{o} dinger operators along tangential curves

Title: On convergence properties for generalized Schr\"{o} dinger operators along tangential curves

Speaker:王会菊（河南大学）

Time:2023-02-09，10:00-11:00

Location:腾讯会议 153460661

Abstract:  In this talk, we consider convergence properties for  generalized Schr\"{o}dinger operators along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schr\{o}dinger operators with polynomial growth along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n \ge 1$. Secondly, it was open until now on pointwise convergence of solutions to the Schr\{o}dinger equation along non-$C^1$ curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n\geq 2$. We develop some new ideas to prove a substitute for the locally constant property, and to make up for lack of translation invariance along time-direction for the related maixmal opertors, which help us to obtain the corresponding results along  some tangential curves when  $n=2$ by the method of induction-on-scales, broad-narrow argument and polynomial partitioning. Moreover, the corresponding convergence rate will follow. Thirdly, we get the convergence results along a family of restricted tangential curves  in $\mathbb{R} \times \mathbb{R}$, which are sharp at two endpoints. As a corollary, we obtain the sharp  $L^p$-Schr\{o}dinger maximal estimates along tangential curves  in $\mathbb{R} \times \mathbb{R}$. This is a joint work with Professor Wenjuan Li.

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