  The Brascamp-Lieb inequalities are a generalization of the H\"older,
Loomis-Whitney, Young, and Finner inequalities that have found many
applications in harmonic analysis and elsewhere. In this paper we introduce an
"adjoint" version of these inequalities, which can be viewed as an $L^p$
version of the entropy Brascamp-Lieb inequalities of Carlen and
Cordero-Erausquin. As applications, we reprove a log-convexity property of the
Gowers uniformity norms, and establish some reverse $L^p$ inequalities for
various tomographic transforms. We conclude with some open questions.
