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