Harmonic Analysis: Calderòn-Zygmund and Beyond : a Conference in Honor of Stephen Vági's Retirement, December 6-8, 2002, DePaul University, Chicago, IllinoisJ. Marshall Ash, Roger L. Jones 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. |
Contents
| 1 | |
On fractional calculus associated to doubling and nondoubling measures | 15 |
Fluids and singular integrals | 39 |
Some recent developments | 53 |
The BMO extended family in product spaces | 63 |
Mean convergence of Cesàro means of Laguerre expansions | 79 |
Common terms and phrases
Amer argument averages ball bidisk BMO(T BMORect(T boundary bounded mean oscillation bounded operator boundedness Bourgain Calderón-Zygmund decomposition Carleson measures Cauchy Cesàro characterization conjecture constant convolution Counterexample defined denote differentiation operator dimensions dn+o dyadic interval dyadic martingale E. M. Stein Eduardo Gatto equal ergodic theory estimate Euler equation fact family of operators finite fluid fractional integral g-variation Hankel operators Hardy spaces harmonic analysis Heisenberg group Hilbert transform holomorphic homogeneous type Kenig kernel Korányi Korteweg–de Vries equation Laguerre Lipschitz martingale maximal function molecule necessary and sufficient nested commutators non-doubling measures norm inequalities obtain Orthogonality lemma Princeton problem product BMO proof properties prove quasidistance rectangles satisfies sequence singular integral operators Sobolev space solutions spaces of homogeneous Stephen Vági sufficient conditions torus variables variation operator weak type weak type 1,1 weight well-posednessSobolev Wierdl Zygmund