Advances In Analysis (ebook)

Argumento de Advances In Analysis (ebook)

Princeton Universitys 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 Steins contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Steins students. The book also includes expository papers on Steins 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.0Preface ix
Chapter 1 Selected Theorems by Eli Stein 1
Charles Fefferman
Chapter 2 Eli?s Impact: A Case Study 35
Charles Fefferman
Chapter 3 On Oscillatory Integral Operators in Higher Dimensions 47
Jean Bourgain
Chapter 4 Hölder Regularity for Generalized Master Equations with Rough Kernels 63
Luis Caffarelli and Luis Silvestre
Chapter 5 Extremizers of a Radon Transform Inequality 84
Michael Christ
Chapter 6 Should We Solve Plateau?s Problem Again? 108
Guy David
Chapter 7 Averages along Polynomial Sequences in Discrete Nilpotent Lie Groups:
Singular Radon Transforms 146
Alexandru D. Ionescu, Akos Magyar, and Stephen Wainger
Chapter 8 Internal DLA for Cylinders 189
David Jerison, Lionel Levine, and Scott Sheffield
Chapter 9 The Energy Critical Wave Equation in 3D 215
Carlos Kenig
Chapter 10 On the Bounded L² Curvature Conjecture 224
Sergiu Klainerman
Chapter 11 On Div-Curl for Higher Order 245
Loredana Lanzani and Andrew S. Raich
Chapter 12 Square Functions and Maximal Operators Associated with Radial Fourier Multipliers 273
Sanghyuk Lee, Keith M. Rogers, and Andreas Seeger
Chapter 13 Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in ?³,
and Newton Polyhedra 303
Detlef Müller
Chapter 14 Multi-Linear Multipliers Associated to Simplexes of Arbitrary Length 346
Camil Muscalu, Terence Tao, and Christoph Thiele
Chapter 15 Diagonal Estimates for Bergman Kernels in Monomial-Type Domains 402
Alexander Nagel and Malabika Pramanik
Chapter 16 On the Singularities of the Pluricomplex Green?s Function 419
D. H. Phong and Jacob Sturm
Chapter 17 Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs 436
Fulvio Ricci
Chapter 18 On Eigenfunction Restriction Estimates and L⁴-Bounds for Compact Surfaces with
Nonpositive Curvature 447
Christopher D. Sogge and Steve Zelditch
List of Contributors 463
Index 465