**CBMS Regional Conference Series in Mathematics**

Volume: 79;
1991;
132 pp;
Softcover

MSC: Primary 42;
Secondary 46

**Print ISBN: 978-0-8218-0731-6
Product Code: CBMS/79**

List Price: $53.00

Individual Price: $42.40

**Electronic ISBN: 978-1-4704-2439-8
Product Code: CBMS/79.E**

List Price: $50.00

Individual Price: $40.00

# Littlewood-Paley Theory and the Study of Function Spaces

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*Michael Frazier; Björn Jawerth; Guido Weiss*

A co-publication of the AMS and CBMS

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.

#### Reviews & Endorsements

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

# Table of Contents

## Littlewood-Paley Theory and the Study of Function Spaces

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface vii8 free
- Introduction 110 free
- 1. Caldeórn's Formula and a Decomposition of L[sup(2)(R[sup(n)]) 716 free
- 2. Decomposition of Lipschitz Spaces 1928
- 3. Minimality of B[sup(0, 1)][sub(1)] 2534
- 4. Littlewood-Paley Theory 3342
- 5. The Besov and Triebel-Lizorkin Spaces 4150
- 6. The φ-Transform 5160
- 7. Wavelets 6170
- 8. Calderón-Zygmund Operators 7584
- 9. Potential Theory and a Result of Muckenhoupt-Wheeden 91100
- 10. Further Applications 99108
- Appendix 113122
- Bibliography 129138
- Back Cover Back Cover1142