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Littlewood-Paley Theory and the Study of Function Spaces
Michael Frazier, Björn Jawerth, University of South Carolina, Columbia, SC, and Guido Weiss, Washington University, St. Louis, MO
A co-publication of the AMS and CBMS.

CBMS Regional Conference Series in Mathematics
1991; 132 pp; softcover
Number: 79
Reprint/Revision History:
reprinted 1997
ISBN-10: 0-8218-0731-5
ISBN-13: 978-0-8218-0731-6
List Price: US$50
Member Price: US$40
All Individuals: US$40
Order Code: CBMS/79
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Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the \(\varphi\)-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets.

The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The \(\varphi\)-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderón-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.


"This monograph is an important and welcome addition to the growing literature in this area."

-- Mathematical Reviews

"Useful for graduate students and researchers with interest in function spaces, approximation theory or wavelet theory."

-- Zentralblatt MATH

Table of Contents

  • Calderón's formula and a decomposition of \(L^2(\mathbb R^n)\) ;
  • Decomposition of Lipschitz spaces;
  • Minimality of \(\dot B^0,1_1\) ;
  • Littlewood-Paley theory;
  • The Besov and Triebel-Lizorkin spaces;
  • The \(\varphi\) -transform;
  • Wavelets;
  • Calderón-Zygmund operators;
  • Potential theory and a result of Muckenhoupt-Wheeden;
  • Further applications.
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