Abstract
In the parallel paper [9] we have introduced “spaces of Wiener’s type”, a family of Banach spaces of (classes of) measurable functions, measures or distributions on locally compact groups. The elements of these spaces are characterized by — what we call — the global behaviour of certain of their local properties. In the present paper it is to be shown that interpolation methods can be applied to these spaces in a very natural way. Using the results on interpolation it is not difficult to extend various theorems of analysis to the setting of Wiener-type spaces. As illustration we present a version of the Hausdorff — Young inequality for locally compact abelian groups. As a consequence, one obtains a sharpened version of Soboley’s embedding theorem.
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© 1981 Birkhäuser Verlag Basel
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Feichtinger, H.G. (1981). Banach Spaces of Distributions of Wiener’s Type and Interpolation. In: Butzer, P.L., Sz.-Nagy, B., Görlich, E. (eds) Functional Analysis and Approximation. ISNM 60: International Series of Numerical Mathematics / ISNM 60: Internationale Schriftenreihe zur Numerischen Mathematik / ISNM 60: Série internationale d’Analyse numérique, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9369-5_16
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DOI: https://doi.org/10.1007/978-3-0348-9369-5_16
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