The L^p estimates of higher order wave operators
数学专题报告
报告题目(Title)：The L^p estimates of higher order wave operators
报告人(Speaker)：尧小华教授（华中师范大学）
地点(Place)：后主楼 1124 （线上腾讯会议号：759905104）
时间(Time)：2023年12月21日下午 14:30-15:30
邀请人(Inviter)：薛庆营
报告摘要
Let H=Δ^2+V be the fourth order Schrodinger operators on R^3 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, Δ^2) are bounded on L^p for all p in (1, ∞) and further that W(H,Δ^2) 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 L^2-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 recent works showing that wave operators W(H, Δ^2) are firstly bounded on L^p for p in (1, ∞) in case of the first kind resonance, and then W(H,Δ^2) are bounded on L^p for p in (1, 3) but unbounded for all p in [3, ∞) in the second and third kind resonance (eigenvalue) cases. The results give sharp L^p boundedness of wave operators on R^3 except for the endpoints cases. Moreover, we also address some progresses of higher order wave operators in other dimensions. These are adjoint -works with H. Haruya and Zijun Wan.
