Abstract
LetG be a noncompact, locally compact group. By means of “generalized dyadic decompositions” ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofL p-spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.
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Feichtinger, H.G. Banach convolution algebras of functions II. Monatshefte f#x00FC;r Mathematik 87, 181–207 (1979). https://doi.org/10.1007/BF01303075
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DOI: https://doi.org/10.1007/BF01303075