Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon

edited by Michael Christ, Carlos E. Kenig and Cora Sadosky

University of Chicago Press, 1999 Cloth: 978-0-226-10456-0 | Paper: 978-0-226-10455-3 Library of Congress Classification QA403.H225 1999 Dewey Decimal Classification 515/.2433

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC

ABOUT THIS BOOK

Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.

In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.

AUTHOR BIOGRAPHY

Michael Christ is professor of mathematics at the University of California, Berkeley. Carlos E. Kenig is the Louis Block Distinguished Service Professor of Mathematics at the University of Chicago. Cora Sadosky is professor of mathematics at Howard University.

TABLE OF CONTENTS

Preface
Introduction
Michael Christ, Carlos E. Kenig, and Cora Sadosky
1. Calderón and Zygmund's Theory of Singular Integrals
Elias M. Stein
2. Transference Principles in Ergodic Theory
Alexandra Bellow
3. A Weak-Type Inequality for Convolution Products
Alexandra Bellow and Alberto P. Calderón
4. Transference Couples and Weighted Maximal Estimates
Earl Berkson, Maciej Paluszynski, and Guido Weiss
5. Periodic Solutions and Nonlinear Wave Equations
Jean Bourgain
6. Some Extremal Problems in Martingale Theory and Ilarmonic Analysis
Donald L. Burkholder
7. The Monge Ampere Equation, Allocation Problems, and Elliptic Systems with Affine Invariance
Luis A. Caffarelli
8. On a Fourth-Order Partial Differential Equation in Conformal Geometry
Sun-Yung A. Chang
9. Riesz Transforms, Commutators, and Stochastic Integrals
A. B. Cruzeiro and P. Malliavin
10. An Application of a Formula of Alberto Calderón to Speaker Identification
Ingrid Daubechies and Stéphane Maes
11. Analytic Capacity, Cauchy Kernel, Menger Curvature, and Rectifiability
Guy David
12. Symplectic Subunit Balls and Algebraic Functions
Charles Fefferman
13. Multiparameter Calderón-Zygmund Theory
Robert A. Fefferman
14. Nodal Sets of Sums of Eigenfunctions
David Jerison and Gilles Lebeau
15. Large-Time Behavior and Self-Similar Solutions of Some Semilinear Diffusion Equations
Yves Meyer
16. Estimates for Elliptic Equations in Unbounded Domains and Applications to Symmetry and Monotonicity
Louis Nirenberg
17. Asymptotic Expansions for Atiyah-Patodi-Singer Problems
Robert Seeley
18. Analysis on Metric Spaces
Stephen Semmes
19. Developments in Inverse Problems since Calderón's Foundational Paper
Gunther Uhlmann
Remarks Addressed to the Conference
Alberto P. Calderón
Contributors
Index

Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon

edited by Michael Christ, Carlos E. Kenig and Cora Sadosky

University of Chicago Press, 1999 Cloth: 978-0-226-10456-0 | Paper: 978-0-226-10455-3

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC

ABOUT THIS BOOK

Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day.

In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.

AUTHOR BIOGRAPHY

Michael Christ is professor of mathematics at the University of California, Berkeley. Carlos E. Kenig is the Louis Block Distinguished Service Professor of Mathematics at the University of Chicago. Cora Sadosky is professor of mathematics at Howard University.

TABLE OF CONTENTS

Preface
Introduction
Michael Christ, Carlos E. Kenig, and Cora Sadosky
1. Calderón and Zygmund's Theory of Singular Integrals
Elias M. Stein
2. Transference Principles in Ergodic Theory
Alexandra Bellow
3. A Weak-Type Inequality for Convolution Products
Alexandra Bellow and Alberto P. Calderón
4. Transference Couples and Weighted Maximal Estimates
Earl Berkson, Maciej Paluszynski, and Guido Weiss
5. Periodic Solutions and Nonlinear Wave Equations
Jean Bourgain
6. Some Extremal Problems in Martingale Theory and Ilarmonic Analysis
Donald L. Burkholder
7. The Monge Ampere Equation, Allocation Problems, and Elliptic Systems with Affine Invariance
Luis A. Caffarelli
8. On a Fourth-Order Partial Differential Equation in Conformal Geometry
Sun-Yung A. Chang
9. Riesz Transforms, Commutators, and Stochastic Integrals
A. B. Cruzeiro and P. Malliavin
10. An Application of a Formula of Alberto Calderón to Speaker Identification
Ingrid Daubechies and Stéphane Maes
11. Analytic Capacity, Cauchy Kernel, Menger Curvature, and Rectifiability
Guy David
12. Symplectic Subunit Balls and Algebraic Functions
Charles Fefferman
13. Multiparameter Calderón-Zygmund Theory
Robert A. Fefferman
14. Nodal Sets of Sums of Eigenfunctions
David Jerison and Gilles Lebeau
15. Large-Time Behavior and Self-Similar Solutions of Some Semilinear Diffusion Equations
Yves Meyer
16. Estimates for Elliptic Equations in Unbounded Domains and Applications to Symmetry and Monotonicity
Louis Nirenberg
17. Asymptotic Expansions for Atiyah-Patodi-Singer Problems
Robert Seeley
18. Analysis on Metric Spaces
Stephen Semmes
19. Developments in Inverse Problems since Calderón's Foundational Paper
Gunther Uhlmann
Remarks Addressed to the Conference
Alberto P. Calderón
Contributors
Index