TY - JOUR
T1 - Adjoint Brascamp-Lieb inequalities
AU - Bennett, Jonathan
AU - Tao, Terence
N1 - Not yet published as of 10/09/2024.
PY - 2024/8/17
Y1 - 2024/8/17
N2 - The Brascamp-Lieb inequalities are a generalization of the Hölder, 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.
AB - The Brascamp-Lieb inequalities are a generalization of the Hölder, 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.
UR - http://www.lms.ac.uk/publication/plms
M3 - Article
SN - 0024-6115
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
ER -