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Optimal Young's inequality and its converse: A simple proof

Abstract : We give a new proof of the sharp form of Young's inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BrLi]. The latter also proved a sharp reverse inequality in the case of exponents less than 1. Our proof is simpler and gives Young's inequality and its converse altogether.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693977
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Submitted on : Thursday, May 3, 2012 - 11:35:39 AM
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Franck Barthe. Optimal Young's inequality and its converse: A simple proof. Geometric And Functional Analysis, Springer Verlag, 1998, 8 (2), pp.234--242. ⟨10.1007/s000390050054⟩. ⟨hal-00693977⟩

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