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Interpolation of Besov spaces. (English) Zbl 0646.46030

The paper deals with Besov spaces \(B^{\alpha}_ q(L_ p)\), which are defined by using the modulus of smoothness. The connections between Besov spaces and approximation by dyadic splines are established. In this way, the spaces \(B^{\alpha}_ q(L_ p)\) are identified with certain sequence spaces. Making use of known results about the interpolation of these sequence spaces [see J. Peetre, New thoughts on Besov spaces; Duke Univ. Math. Ser. I (1976; Zbl 0356.46038)] the authors obtain interpolation theorems for Besov spaces.
Reviewer: B.Opic

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A15 Spline approximation
46M35 Abstract interpolation of topological vector spaces
41A63 Multidimensional problems
46A45 Sequence spaces (including Köthe sequence spaces)

Citations:

Zbl 0356.46038
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References:

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