報告人：李平（長江大學）

報告題目：Lp boundedness of wave operators for high-order Schrödinger operators on the line

報告摘要：In this paper, we are mainly devoted to investigating the Lp boundedness of wave operators $W_\pm$ associated with high-order Schrödinger operators $H=(-\Delta)^m+V(x)$ with $m \geq 3$ in dimension one when zero is a regular point. Under a suitable decay condition on potential V, we established a general conclusion covering the already known results for the cases $m=1,2$ by a unified method. Specifically, our results are twofold: for the non-endpoint case, we  have obtained that $W_\pm \in B(L^p(w_p))$ for any $1< p< \infty$, $w_p\in A_p$; and for the endpoint situation, $W_\pm\in B(H^1(R)$, $L^1(R)\bigcap B(L^\infty, BMO(R)))$ and if suppV is compact $W_\pm\notin B(L^1(R))$, but $W_\pm\notin B(L^1(R))$, and generally $W_\pm\notin B(L^\infty(R))$. This work is joint with S. Chen,S. Huang and X. Yao.

報告時間：2024年10月11日（星期五）16:00-18:00

報告地點：科技樓南607室

邀請人：黃山林

報告人簡介：李平，長江大學信息與數學學院，副教授，目前主持國家基金面上項目一項；研究方向為調和分析及其應用、非交換調和分析；近年來聚焦于高階薛定谔算子的色散估計、高階波方程的色散估計、非交換調和分析的研究，取得了一系列原創性成果，這些成果部分發表于Journal of Functional Analysis，J. Diffferential Equations, Communications on Pure and Applied Analysis等期刊上。