A Hausdorff-young Inequality for Measured Groupoids
نویسندگان
چکیده
The classical Hausdorff-Young inequality for locally compact abelian groups states that, for 1 ≤ p ≤ 2, the L-norm of a function dominates the L-norm of its Fourier transform, where 1/p + 1/q = 1. By using the theory of non-commutative L-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-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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