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Harmonic Analysis

Calderon-Zygmund and Beyond

illustrated Edition

J.Marshall Ash (editor) Roger L. Jones (editor)

ISBN: 9780821839201

Publication Date: Aug 2006

Format: Paperback

Also available as: Hardback  

Suitable for those interested in harmonic analysis and its application to partial differential equations and ergodic theory. This book describes developments in harmonic analysis: Eduardo Gatto studies spaces with doubling and non-doubling measures; Cora Sadosky, product spaces; and Benjamin Muckenhoupt, Laguerre expansions.

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Starting in the early 1950's, Alberto Calderon, 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 Vagi upon his retirement in 2002. Vagi was a student of Calderon in the 1960's, when Calderon and Zygmund were at their peak. Two authors, Kenig and Gatto, were students of Calderon; 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 Calderon-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 Koranyi summarizes Vagi'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.
Illustrations Illustrations
Pages 147
Date Published 30 Aug 2006
Publisher American Mathematical Society
Series Contemporary Mathematics
Series Part No. 411
Subject/s Calculus & mathematical analysis   Functional analysis & transforms   Applied mathematics   Differential calculus & equations   Real analysis, real variables   Fluid mechanics  
The work of Stephen Vagi by A. Koranyi On fractional calculus associated to doubling and non-doubling measures by A. E. Gatto Fluids and singular integrals by C. Fefferman The well-posedness of non-linear dispersive equations: Some recent developments by C. Kenig The BMO extended family in product spaces by C. Sadosky Mean convergence of Cesaro means of Laguerre expansions by B. Muckenhoupt Variation inequalities for singular integrals and related operators by R. L. Jones A maximal function on the discrete Heisenberg group with applications to ergodic theory by S. Wainger Problems by B. Muckenhoupt, R. L. Jones, P. Janakiraman, D. Ryabogin, and J. Xiao.

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