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Journal Articles Geometric And Functional Analysis Year : 1998

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.

Dates and versions

hal-00693977 , version 1 (03-05-2012)

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Franck Barthe. Optimal Young's inequality and its converse: A simple proof. Geometric And Functional Analysis, 1998, 8 (2), pp.234--242. ⟨10.1007/s000390050054⟩. ⟨hal-00693977⟩
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