This paper studies Hausdorff--Young inequalities for certain group extensions, by use of Mackey's theory. We consider the case in which the dual action of the quotient group is free almost everywhere. This result applies in particular to yield a Hausdorff--Young inequality for nonunimodular groups.

MSC Classifications:

43A30, 43A15 show english descriptions Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
$L^p$-spaces and other function spaces on groups, semigroups, etc. 43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.

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