Recent developments in the theory of function spaces. (English) Zbl 0611.46036

Differential equations and their applications, Equadiff. 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 95-106 (1986).
[For the entire collection see Zbl 0595.00009.]
The author of this paper has many contributions to unify and simplify the theory of function spaces. This notion ”function spaces”, means here spaces of functions and distributions, defined on the real Euclidean n- space \(R^ n\), which are isotropic, nonhomogeneous and unweighted.
So, H. Triebel, in ”Spaces of Besov-Hardy-Sobolev type” (1978; Zbl 0408.46024) or in ”Theory of function spaces” (1983; Zbl 0546.46027), but especially in J. Approx. Theory 35, 275-297 (1982; Zbl 0487.46013), has proved that there exists a unified approach, which covers all the methods, apparently rather different, via derivatives, differences, Fourier analytical decompositions, harmonic and thermic extensions, which yield the same spaces \(B^ s_{p,q}\) and \(F^ s_{p,q}.\)
In this paper the author gets some theorems, in order to unify and simplify the theory of function spaces and in order to serve as a starting point for further studies, too.
Reviewer: A.Donescu


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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