报告题目：The L^p-boundedness of wave operators for fourth order Schr\"odinger operator on the line
报 告 人：尧小华
工作单位：华中师范大学数学与统计学院
报告时间：2022-9-26 15:00-17:00；
腾讯会议ID：993511434
报告摘要：
In this talk we will consider the L^p-bounds of wave operators W(H, \triangle^2) associated with bi-Schr\"odinger operators H=\triangle^2+V(x) on R. Under a suitable decay condition on Vand the absence of embedded eigenvalues of H, we first prove that the wave and dual wave operators are bounded on L^p(R) for all 1<p<\infity. This result is further extended to the weighted L^p-boundedness with the sharp A_p-bounds for general even A_p-weights and to the boundedness on the Sobolev spaces W^{s,p}(R). For the limiting case p=1, we also obtain several weak-type boundedness, including W(H, \triangle^2) being contained in B(L^1,L^\infity and B(H^1,L^1). These results especially hold whatever the zero energy is a regular point or a resonance. Next, for the case that zero is a regular point, we prove that the wave operators are neither bounded on L^1(R) nor on L^\infity(R), and they are even not bounded from L^(R) to BMO(R) if V is compactly supported. Finally, as applications, we can deduce the L^p-L^qdecay estimates for the propagator e^{-itH}with pairs (1/p,1/q)belonging to certain region of R^2, as well as the H\"ormander-type L^p-boundedness theorem for the spectral multiplier f(H).
报告人简介：
尧小华，华中师范大学教授，博士生导师。研究方向为调和分析与偏微分算子，研究兴趣主要集中在调和分析与偏微分方程的交叉领域，并主持和承担过包括国家自然科学面上基金、新世纪优秀人才计划项目在内的多项科研项目。自2001年以来，在Comm. Math. Phys.、J. Funct. Anal、J. Differential Equations、Comm. Partial Differential Equations等期刊发表一系列重要研究成果。
