A Hausdorff-Young inequality for measured groupoids

Details A Hausdorff-Young inequality for measured groupoids A Hausdorff-Young inequality for measured groupoids

2008-03-15

arxiv.org/abs/0803.2282v1

Mathematics

Operator Algebras

10 pages, a talk at 2007 Sibiu Conference on von Neumann algebras, operator spaces and free probability theory

Scientific paper

The classical Hausdorff-Young inequality for locally compact abelian groups states that, for $1\le p\le 2$, the $L^p$-norm of a function dominates the $L^q$-norm of its Fourier transform, where $1/p+1/q=1$. By using the theory of non-commutative $L^p$-spaces and by reinterpreting the Fourier transform, R. Kunze (1958) [resp. M. Terp (1980)] extended this inequality to unimodular [resp. non-unimodular] groups. The analysis of the $L^p$-spaces of the von Neumann algebra of a measured groupoid provides a further extension of the Hausdorff-Young inequality to measured groupoids.

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