报告题目：四阶Schrodinger算子的波算子的L^P估计

报告人：尧小华  教授

工作单位：华中师范大学

报告时间：2023年12月02日   9:00-10:00

报告地点：七乐彩中奖 305

Let H=Δ²+V be the fourth order Schrodinger operators on R³ with real fast decay potentials. If zero is neither a resonance nor an eigenvalue of  H, then it was recently proved that wave operators  W(H+Δ²)  are bounded on  L^P for all 1<p<∞ and further that W(H,Δ²) are unbounded on the endpoint spaces p=1 and ∞. However, note that even if  V is a compactly supported potential, zero resonance or eigenvalue of H possibly happens due to the existence of some nonzero solution of Hf=0 in a suitable L²-weighted spaces. So it would be interesting to further establish L^P-bounds of wave operators with zero threshold singularities.  In this talk, we will talk about some works showing that wave operators W(H,Δ²) are firstly bounded on L^P for 1<p<∞ in case of the first kind resonance, and then  W(H,Δ²) are bounded on  L^P for 1<p<3 but unbounded for all 3≤p<∞ in the second and third kind resonance (eigenvalue) cases. The results give sharp L^P boundedness of wave operators on R³ except for the endpoints cases. Moreover, we also address some progresses of higher order wave operators in other dimensions.

报告人简介：

尧小华，华中师范大学数学与统计学学院教授，博士生导师；2010年入选教育部新世纪人才支持计划，主要从事调和分析与微分算子的研究，围绕薛定谔算子的色散估计、孤立子的稳定性等问题开展科研工作，论文发表在Comm. Math. Phys.、Trans. AMS.、Ann. H. Poincare、J. Funct. Anal.等国际数学期刊上；目前连续主持国家基金委面上项目3项，曾主持教育部重点项目1项，参与了教育部偏微分方程长江学者创新团队的建设。学术上先后访问过美国Johns Hopkins大学、普林斯顿高等研究所、新泽西罗格斯大学等高校。

欢迎大家参加！