Abstract
The Hausdorff–Young inequality is well known for the Fourier transform in R n . More recently, Hausdorff–Young inequalities were established for unimodular groups (Kunze, 1958) and non-unimodular groups (Terp, 1980). A version was also given for X × X by Russo (1977), where X denotes a measured space. In this Note, we first study the L p -spaces of the von Neumann algebra of a groupoid, and propose identifications of some of them as function spaces. Using interpolation, we then give a Hausdorff–Young inequality for groupoids. To cite this article: P. Boivin, C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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