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Sharp local smoothing estimates for Fourier integral operators
发布时间: 2018-12-29     15:39   【返回上一页】 发布人:Christopher D. Sogge


调和分析专题报告

 

 

 

报告题目: Sharp local smoothing estimates for Fourier integral operators

 

报告人:Christopher D. Sogge 教授(Johns Hopkins University, USA)

 

邀请人:徐桂香

 

时间地点 2019年1月15日 15:00 - 16:00,后主楼 1124

 

摘要:We present joint work with D. Beltran and J. Hickman on sharp local smoothing estimates for general Fourier integral operators. Local smoothing bounds imply major estimates in harmonic analysis, including Bochner-Riesz estimates, oscillatory integral estimates and bounds for the size of Besicovitch sets and related problems involving Kakeya maximal functions. Our work gives a sharp resolution to the most general form of the local smoothing problem formulated by the speaker in the early 1990s.  We rely on decoupling estimates of Bourgain and Demeter.

 

个人简介:Chris Sogge教授1982年本科毕业于芝加哥大学,1985年博士毕业于普林斯顿大学,师从E.M.Stein教授,是调和分析领域Stein学派重要代表人物,是杰出的调和分析与偏微分方程专家,Chris Sogge教授在Fourier积分算子理论、限制性定理、波动方程Strichartz估计及流形上Laplacian算子特征函数估计等领域做出一系列杰出的学术成果,出版专著《Lectures on Nonlinear Wave Equations》、《Fourier Integrals in Classical Analysis》、《Hangzhou Lectures on Eigenfunctions of the Laplacian》。已发表100余篇学术论文,其中十余篇学术论文发表在Acta. Math., Ann. Math., J. Amer. Math. Soc., Invent. Math.顶级期刊。Chris Sogge教授获得如下学术荣誉:

1985 NSF Postdoctoral Fellowship, 1985

1988 Sloan Fellowship, Presidential Young Investigator Award  

1994 Invited speaker, International Congress of Mathematicians, Zurich

2005 Guggenheim Fellow

2007 Johns Hopkins Diversity Recognition Award

2012-13 Simons Fellow

2013 Fellow, American Mathematical Society

2014 Professor of the Year, JHU Mathematics Department