Harmonic Analysis: Calderon-Zygmund and Beyond

Starting in the early 1950's, Alberto Calderón, Antoni Zygmund, and their students developed a program in harmonic analysis with far-reaching consequences. The title of these proceedings reflects this broad reach. This book came out of a DePaul University conference honoring Stephen Vági upon his retirement in 2002. Vági was a student of Calderón in the 1960's, when Calderón and Zygmund were at their peak. Two authors, Kenig and Gatto, were students of Calderón; one, Muckenhoupt, was a student of Zygmund. Two others studied under Zygmund's student Elias Stein. The remaining authors all have close connections with the Calderón-Zygmund school of analysis. This book should interest specialists in harmonic analysis and those curious to see it applied to partial differential equations and ergodic theory. In the first article, Adam Korányi summarizes Vági's work. Four additional articles cover various recent developments in harmonic analysis: Eduardo Gatto studies spaces with doubling and non-doubling measures; Cora Sadosky, product spaces; Benjamin Muckenhoupt, Laguerre expansions; and Roger Jones, singular integrals. Charles Fefferman and Carlos Kenig present applications to partial differential equations and Stephen Wainger gives an application to ergodic theory. The final article records some interesting open questions from a problem session that concluded the conference