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Littlewood-Paley Theory and the Study of Function Spaces

Björn Jawerth University of South Carolina, Columbia, SC
Guido Weiss Washington University, St. Louis, MO
A co-publication of the AMS and CBMS
Available Formats:
Softcover 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
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List Price: $79.50 Click above image for expanded view Littlewood-Paley Theory and the Study of Function Spaces Björn Jawerth University of South Carolina, Columbia, SC Guido Weiss Washington University, St. Louis, MO A co-publication of the AMS and CBMS Available Formats:  Softcover 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 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$79.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 791991; 132 pp
MSC: Primary 42; Secondary 46;

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.

• Chapters
• 1. Introduction
• 1. Calderón’s Formula and a Decomposition of $L^2(\mathbb {R}^n)$
• 2. Decomposition of Lipschitz Spaces
• 3. Minimality of $\dot {B}_1^{0, 1}$
• 4. Littlewood-Paley Theory
• 5. The Besov and Triebel-Lizorkin Spaces
• 6. The $\phi$-Transform
• 7. Wavelets
• 8. Calderón-Zygmund Operators
• 9. Potential Theory and a Result of Muckenhoupt-Wheeden
• 10. Further Applications
• 12. Appendix
• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 791991; 132 pp
MSC: Primary 42; Secondary 46;

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.

• Chapters
• 1. Introduction
• 1. Calderón’s Formula and a Decomposition of $L^2(\mathbb {R}^n)$
• 2. Decomposition of Lipschitz Spaces
• 3. Minimality of $\dot {B}_1^{0, 1}$
• 4. Littlewood-Paley Theory
• 5. The Besov and Triebel-Lizorkin Spaces
• 6. The $\phi$-Transform
• 7. Wavelets
• 8. Calderón-Zygmund Operators
• 9. Potential Theory and a Result of Muckenhoupt-Wheeden
• 10. Further Applications
• 12. Appendix
• 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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