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 Lp boundedness of wave operators for high-order Schr?dinger operators on the line

主讲人：李平

摘要：In this paper, we are mainly devoted to investigating the Lp boundedness of wave operators $W_\pm$ associated with high-order Schr?dinger 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.

主讲人简介：李平，长江大学信息与数学学院，副教授，目前主持国家基金面上项目一项；研究方向为调和分析及其应用、非交换调和分析；近年来聚焦于高阶薛定谔算子的色散估计、高阶波方程的色散估计、非交换调和分析的研究，取得了一系列原创性成果，这些成果部分发表于Journal of Functional Analysis，J. Diffferential Equations, Communications on Pure and Applied Analysis等期刊上。

邀请人：黄山林

时间：2024年10月11日（星期五）16:00-18:00

地点：科技楼南607室