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Euclidean Forward-Reverse Brascamp-Lieb Inequalities: Finiteness, Structure and Extremals (1907.12723v2)
Published 30 Jul 2019 in math.FA, cs.IT, math.CA, and math.IT
Abstract: A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed, which generalizes the fact that the best constants in the Brascamp-Lieb and Barthe inequalities are equal. Finally, as the title hints, the main results concerning finiteness, structure and gaussian-extremizability for the Brascamp-Lieb inequality due to Bennett, Carbery, Christ and Tao are generalized to the setting of the forward-reverse Brascamp-Lieb inequality.