Banach Spaces of Distributions of Wiener’s Type and Interpolation

Abstract

Wien In the parallel pa~ [9] we have introducerl "spaces of Wiener's type", a family of Banach spaces of (classes of) neasurable functions, measures or distributions on locally carpact groups. The elenents of these spaces are cha-racterizerl by-what we call-the global behaviour of certain of their local properties. In the present pa~ it is to be shown that interpolation rrethods can be applierl 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 canpact abelian groups. As a consequerx:e, one obtains a sharpenErl version of Sobolev's erberlding theorem.