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On vector-valued Hörmander-Beurling spaces. (English) Zbl 1057.46030

The author extends Hörmander-Beurling spaces to the vector-valued setting and studies some of their properties: he calculates the dual of \(B_{p,k}(E)\) without supposing that \(E'\) possesses the Radon-Nikodým property, he generalizes Favini’s result about interpolation of Hörmander spaces, and he proves that the spaces \(B_{p,k}(E)\) and \(B_{\infty,k}^0 (E)\) have the property of approximation by cutting.
Reviewer: Josef Wloka (Kiel)

MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions
46E40 Spaces of vector- and operator-valued functions
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