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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
Littlewood-Paley Theory and the Study of Function Spaces
Softcover ISBN:  978-0-8218-0731-6
Product Code:  CBMS/79
List Price: $56.00
Individual Price: $44.80
eBook ISBN:  978-1-4704-2439-8
Product Code:  CBMS/79.E
List Price: $53.00
Individual Price: $42.40
Softcover ISBN:  978-0-8218-0731-6
eBook: ISBN:  978-1-4704-2439-8
Product Code:  CBMS/79.B
List Price: $109.00 $82.50
Littlewood-Paley Theory and the Study of Function Spaces
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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
Softcover ISBN:  978-0-8218-0731-6
Product Code:  CBMS/79
List Price: $56.00
Individual Price: $44.80
eBook ISBN:  978-1-4704-2439-8
Product Code:  CBMS/79.E
List Price: $53.00
Individual Price: $42.40
Softcover ISBN:  978-0-8218-0731-6
eBook ISBN:  978-1-4704-2439-8
Product Code:  CBMS/79.B
List Price: $109.00 $82.50
  • 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.

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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 publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.