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

Franck Barthe (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Physique mathématique [math-ph]

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⟩