Strong Brascamp-Lieb Inequalities

02/13/2021

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by   Lei Yu, et al.

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In this paper, we derive sharp nonlinear dimension-free Brascamp-Lieb inequalities (including hypercontractivity inequalities) for distributions on Polish spaces, which strengthen the classic Brascamp-Lieb inequalities. Applications include the generalization of Mr. and Mrs. Gerber's lemmas to Rényi entropies and distributions on Polish spaces, the strengthening of small-set expansion theorems, and the characterization of the exponent of q-stability of Boolean functions. Our proofs in this paper are based on information-theoretic techniques and coupling techniques.