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Bounded and compact integral operators. (English) Zbl 1023.42001
Mathematics and its Applications (Dordrecht). 543. Dordrecht: Kluwer Academic Publishers. xvi, 643 p. (2002).
This fundamental monograph is written by well-known experts. It presents some of the authors’ results about boundedness, compactness and other properties of important integral operators in one and many dimensions arising in harmonic analysis and theory of function spaces. Among these operators are Hardy type operators, fractional integrals and maximal functions of different types, operators of the potential type, singular integral operators, Fourier multipliers. The main focus is the action of these operators in a large scale of weighted spaces of Lebesgue type. A special chapter is devoted to open problems. The book will certainly be useful for researchers in harmonic analysis and related areas.

42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
42A50 Conjugate functions, conjugate series, singular integrals
42B15 Multipliers for harmonic analysis in several variables
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
47G10 Integral operators