应304am永利集团官网耿俊教授和杨四辈教授邀请, 华中师范大学尧小华教授将于2022年10月13日举行线上专题学术报告.

报告题目：The L^p-boundedness of wave operators for fourth order Schrödinger operator

时 间：2022年10月13日(星期四)14:30

腾讯会议ID: 115-692-757

报告摘要：

In this talk we will consider the L^p-bounds of wave operators W(H,) associated with bi-Schrödinger 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<p<. 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 Hörmander-type L^p-boundedness theorem for the spectral multiplier f(H). This is a joint-work with H. Mizutani and Zijun Wan.

欢迎广大师生参加！

尧小华教授简介

尧小华, 华中师范大学304am永利集团官网教授、博士生导师, 2010年入选教育部新世纪人才计划; 主要从事调和分析与微分算子的研究; 在色散方程、微分算子及函数空间等方向上开展研究工作; 主要学术成果发表在“Comm. Math. Phys.”、 “Trans. AMS”、 “Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、 Siam J. Math. Anal.等国际重要数学期刊上; 连续主持过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; 作为核心成员参与了华中师范大学教育部长江学者及创新团队(偏微分方程)建设.

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室

304am永利集团官网

萃英学院

2022年10月10日