Littlewood-Paley theory and the study of function spaces
Author(s)
Bibliographic Information
Littlewood-Paley theory and the study of function spaces
（Regional conference series in mathematics, no. 79）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1991
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Note
"Based on lectures given in July of 1989 at a regional conference in Auburn University" -- Pref
"Expository lectures from the CBMS Regional Conference held at Auburn University, July 3-7, 1989" -- T.p. verso
Bibliography p. 129-132
Description and Table of Contents
Description
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 (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.
Table of Contents
- Calderon'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
- Calderon-Zygmund operators
- Potential theory and a result of Muckenhoupt-Wheeden
- Further applications.
by "Nielsen BookData"