Advances in Analysis

Charles Fefferman; Alexandru D. Ionescu; D.H. Phong; Stephen Wainger

Charles Fefferman, Alexandru D. Ionescu, D.H. Phong and Stephen Wainger

Advances in Analysis

The Legacy of Elias M. Stein (PMS-50)

In: Princeton Mathematical Series

Princeton University Press | 2014

https://doi.org/10.1515/9781400848935

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Contents

About this book

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein’s contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Stein’s students. The book also includes expository papers on Stein’s work and its influence.

The contributors are Jean Bourgain, Luis Caffarelli, Michael Christ, Guy David, Charles Fefferman, Alexandru D. Ionescu, David Jerison, Carlos Kenig, Sergiu Klainerman, Loredana Lanzani, Sanghyuk Lee, Lionel Levine, Akos Magyar, Detlef Müller, Camil Muscalu, Alexander Nagel, D. H. Phong, Malabika Pramanik, Andrew S. Raich, Fulvio Ricci, Keith M. Rogers, Andreas Seeger, Scott Sheffield, Luis Silvestre, Christopher D. Sogge, Jacob Sturm, Terence Tao, Christoph Thiele, Stephen Wainger, and Steven Zelditch.

Author information

Charles Fefferman and Alexandru D. Ionescu are professors of mathematics at Princeton University. D. H. Phong is professor of mathematics at Columbia University. Stephen Wainger is professor emeritus of mathematics at the University of Wisconsin-Madison.

Frontmatter Free access PDF PDF	i
Contents Free access PDF PDF	vii
Preface Access restricted Content is available PDF PDF	ix
Chapter One. Selected Theorems by Eli Stein Charles Fefferman Access restricted Content is available PDF PDF	1
Chapter Two. Eli’s Impact: A Case Study Charles Fefferman Access restricted Content is available PDF PDF	35
Chapter Three On Oscillatory Integral Operators in Higher Dimensions Jean Bourgain Access restricted Content is available PDF PDF	47
Chapter Four. Hölder Regularity for Generalized Master Equations with Rough Kernels Luis Caffarelli and Luis Silvestre Access restricted Content is available PDF PDF	63
Chapter Five. Extremizers of a Radon Transform Inequality Michael Christ Access restricted Content is available PDF PDF	84
Chapter Six. Should We Solve Plateau’s Problem Again? Guy David Access restricted Content is available PDF PDF	108
Chapter Seven. Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups: Singular Radon Transforms Alexandru D. Ionescu, Akos Magyar and Stephen Wainger Access restricted Content is available PDF PDF	146
Chapter Eight. Internal DLA for Cylinders David Jerison, Lionel Levine and Scott Sheffield Access restricted Content is available PDF PDF	189
Chapter Nine. The Energy Critical Wave Equation in 3D Carlos Kenig Access restricted Content is available PDF PDF	215
Chapter Ten. On the Bounded L2 Curvature Conjecture Sergiu Klainerman Access restricted Content is available PDF PDF	224
Chapter Eleven. On Div-Curl for Higher Order Loredana Lanzani and Andrew S. Raich Access restricted Content is available PDF PDF	245
Chapter Twelve. Square Functions and Maximal Operators Associated with Radial Fourier Multipliers Sanghyuk Lee, Keith M. Rogers and Andreas Seeger Access restricted Content is available PDF PDF	273
Chapter Thirteen. Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller Access restricted Content is available PDF PDF	303
Chapter Fourteen. Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length Camil Muscalu, Terence Tao and Christoph Thiele Access restricted Content is available PDF PDF	346
Chapter Fifteen. Diagonal Estimates for Bergman Kernels in Monomial-Type Domains Alexander Nagel and Malabika Pramanik Access restricted Content is available PDF PDF	402
Chapter Sixteen. On the Singularities of the Pluricomplex Green’s Function D. H. Phong and Jacob Sturm Access restricted Content is available PDF PDF	419
Chapter Seventeen. Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs Fulvio Ricci Access restricted Content is available PDF PDF	436
Chapter Eighteen. On Eigenfunction Restriction Estimates and L4-Bounds for Compact Surfaces with Nonpositive Curvature Christopher D. Sogge and Steve Zelditch Access restricted Content is available PDF PDF	447
List of Contributors Access restricted Content is available PDF PDF	463
Index Access restricted Content is available PDF PDF	465

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Advances in Analysis

The Legacy of Elias M. Stein (PMS-50)

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