Advances in Analysis: The Legacy of Elias M. Stein

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Princeton University Press, Jan 5, 2014 - Mathematics - 480 pages

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.

 

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Contents

A Case Study
35
Hölder Regularity for Generalized Master Equations with
63
Extremizers of a Radon Transform Inequality
84
Should We Solve Plateaus Problem Again?
108
Averages along Polynomial Sequences in Discrete Nilpotent
146
Internal DLA for Cylinders
189
The Energy Critical Wave Equation in 3D
215
On DivCurl for Higher Order
245
CONTENTS
273
Problems of Harmonic Analysis Related to FiniteType
303
MultiLinear Multipliers Associated to Simplexes of Arbitrary
346
Diagonal Estimates for Bergman Kernels in MonomialType
402
On the Singularities of the Pluricomplex Greens Function
419
Smoothness of Spectral Multipliers and Convolution Kernels
436
List of Contributors
463
Copyright

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About the author (2014)

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.

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