Euclidean Forward–Reverse Brascamp–Lieb Inequalities: Finiteness, Structure, and Extremals
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12220_2020_398_ReferencePDF.pdf
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801c7570a3fde3a246ceb7d913a81a85
Author(s)
Courtade, Thomas A
Liu, Jingbo
Date Issued
March 30, 2020
Publisher
Springer US
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s12220-020-00398-y
