On the L^p estimates of higher order wave operators

主讲人：尧小华

摘要：In this talk we will consider the L^p-bounds of wave operators W(H, Δ^2) associated with bi-Schr\"odinger operators H=Δ^2+V(x) on the line. 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<∞. For the limiting case p=1, we also obtain several weak-type boundedness, including W(H, Δ^2)∈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. As applications, the L^p-L^q decay estimates for the propagator e^{-itH}and the H\"ormander-type L^p-boundedness for multiplier f(H) are given. Moreover, we also list some progresses of higher order wave operators in other dimensions. These are joint-works with H. Mizutani and Zijun Wan.

主讲人简介：尧小华, 华中师范大学数学与统计学院教授、博士生导师, 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。

邀请人：黄山林

时间：2023年6月13日（星期二）9:00-11:00