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LittlewoodPaley 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 NSFCBMS 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 LittlewoodPaley 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 LittlewoodPaley theory. The $varphi$transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (CalderonZygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.
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birth defects, or other reproductive harm.
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