Orthonormal Strichartz estimates in Dunkl setting

：宋曼利（西北工业大学）
：2025-07-16 16:30
：海韵园实验楼S102

报告人：宋曼利（西北工业大学）

时  间：2025年7月16日10:30

地  点：海韵园实验楼S102

内容摘要:

Since the pioneering work by Frank-Lewin-Lieb-Seiringer [J. Eur. Math. Soc., 2014] and Frank-Sabin [Amer. J.. Math, 2017], substantial attention has been devoted by numerous researchers to extending single-function Strichartz estimates to versions involving systems of orthonormal functions in a given Hilbert space, such as the Lebesgue space L²(Rⁿ) or the homogeneous Sobolev space H^s(Rⁿ). In this talk, we introduce Strichartz estimates involving orthonormal systems in the Dunkl setting. It contains three parts. Firstly, we obtain the orthonormal Strichartz estimates for the Dunkl-Schodinger operator in L_κ²(Rⁿ). Next, we consider the case of orthonormal systems in the homogeneous space H_κ^s(Rⁿ). Finally, we establish maximal estimates with respect to the spatial variable, which are certain boundary cases of the second part. These results are generalization of the work Frank-Sabin [Amer.J..Math., 2017], Bez-Hong-Lee-Nakamura-Sawano [Adv. Math., 2019] and Bez-Kinoshita-Shiraki [Trans. London. Math. Soc.,2024] in the Dunkl setting.

个人简介：

宋曼利，西北工业大学数学与统计学院副教授，硕士生导师。2014年7月博士毕业于北京大学；2012年9月-2014年2月在国家留学基金委资助下赴德国基尔大学博士联合培养，合作导师Detlef Müller教授。研究方向为调和分析及其在偏微分方程中的应用，主持国家自然科学基金1项，中国博士后基金1项，中央高校基金2项，陕西省基金2项。在Israel J. Math., J.Geom. Anal. Pacific J. Math.等数学专业期刊发表论文多篇。

 

联系人：伍火熊