一、报告题目：The L^p-boundedness of wave operators for fourth order Schrodinger operator on the line

二、报告人：尧小华 教授

三、时 间：2022 年 4 月 17 日 (周日)上午  10:30---11:20.

四、腾讯会议号：762-7964-8189,  线下地点: 太阳成集团tyc122ccA4-311

五、报告摘要：In this talk we will consider the L^p-bounds of wave operators W(H,) associated with bi-Schr\"odinger operators H=+V(x) on R. Under a suitable decay condition on V and 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. 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,)B(L^1, L^) 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^(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^q decay 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, 华中师范大学数学与统计学院教授、博士生导师，2011年入选教育部新世纪人才计划；作为高级访问学者曾在美国Johns Hopkins大学留学一年；主要从事调和分析与微分算子领域的研究；目前在微分算子色散估计和非线性薛定谔方程孤立子稳定性问题上开展研工作；主要成果发表在“Comm. Math. Phys.”、 “Trans. AMS”、 “Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、“Siam J. Math. Anal.” “Siam J. Appl. Math.”等多个国际数学期刊上；连续主持多项国家自然科学基金面上项目，也曾主持过教育部科学技术研究重点项目及新世纪优秀人才计划等多个科研项目；作为成员也参与了华中师范大学教育部长江学者创新团队（偏微分方程）的建设。

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