  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.
