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Topics in Fourier analysis and function spaces. (English) Zbl 0661.46024
Mathematik und ihre Anwendungen in Physik und Technik, Bd. 42. Leipzig: Akademische Verlagsgesellschaft Geest & Portig K.-G. 300 p.; M 71.00 (1987).
The second author of the present book is well-known all over the world not only as a leading specialist in functional analysis, operator theory, and differential equations, but also as author of several books on function spaces and applications which have become standard references. The two monographs [“Interpolation theory, function spaces, differential operators” (1978; Zbl 0387.46032) and “Theory of function spaces” (1978; Zbl 0546.46027)] dealt mainly with isotropic spaces of Besov- Hardy-Sobolev type on \({\mathbb{R}}^ n\) and on smooth domains. The present book is concerned with other classes of function spaces of this type, such as periodic, weighted, or anisotropic spaces; much material was published before only in research articles. In another part, the authors discuss related spaces of entire analytic functions; this may be considered as an updated version of the corresponding chapters in the second author’s book [“Fourier analysis and function spaces” (1977; Zbl 0345.42003)].
Reviewer: J.Appell

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E15 Banach spaces of continuous, differentiable or analytic functions
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces