2019-09-02 16:13 李文娟 宋曼利  理学院 审核人:   (点击: )

报告题目:Maximal operators associated to hypersurfaces in R^3

报告人:德国基尔大学Stefan Buschenhenke博士




报告摘要:We discuss L^p bounds for maximal operators associated to two-dimensional surfaces in R^n and present an overview on recent results. In certain cases, depending on the so-called height and on the number of vanishing principal curvatures, this leads to the study of a certain class of Fourier multipliers, which behave similar to cone multipliers, but are intertwined with an oscillatory Fourier integral operator. We discuss properties, bounds and conjectures for this new class of operators. The conjectured L^4 bound seems to be of similar difficulty as for the cone multiplier, but we can prove a analogus result for a lower-dimensional multiplier. This is joint work with Spyros Dendrinos, Isroil Ikromov and Detlef Müller.

报告人简介:Stefan Buschenhenke博士于2014年4月毕业于德国基尔大学。2014年5月-10月在西班牙数学研究所Instituto de Ciencias Mathematicas做博士后;2014年10月-2016年9月在德国基尔大学做博士后;2016年9月-2018年3月在英国伯明翰大学做博士后;2018年4月至今在德国基尔大学做博士后。他一直潜心钻研调和分析四大猜想方面的问题,如限制性定理和与曲面相关的极大函数等,目前与众多著名调和分析专家A. Vargas, D. Mueller, J. Bennett, M. Cowling,I. Ikoromov合作著有十余篇与其相关的论文,发表在如J. Diff. Equal.等著名期刊上。