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Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces. (English) Zbl 0806.42013

Mem. Am. Math. Soc. 530, 126 p. (1994).
The concept of space of homogeneous type was introduced by R. R. Coifman and G. Weiss as the natural frame for a general Calderón-Zygmund theory [“Analyse harmonique noncommutative sur certains espaces homogènes” (1971; Zbl 0224.43006)]. The authors develop a version of Littlewood-Paley theory in this general context. Their analogue of the Littlewood-Paley decomposition is based on a construction of G. David, J. L. Journé and S. Semmes [Rev. Mat. Iberoam. 1, No. 4, 1-56 (1985; Zbl 0604.42014)]. The authors prove a suitable analogue of the Calderón reproducing formula and apply it to study Besov- and Triebel-Lizorkin spaces defined via the generalized Littlewood-Paley decompositions.
Reviewer: A.Seeger (Madison)

MSC:

42B25 Maximal functions, Littlewood-Paley theory
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B30 \(H^p\)-spaces
42B15 Multipliers for harmonic analysis in several variables
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