OPTIMAL YOUNGS-INEQUALITY AND ITS CONVERSE - A SIMPLE PROOF

Authors
BARTHE F
Citation
F. Barthe, OPTIMAL YOUNGS-INEQUALITY AND ITS CONVERSE - A SIMPLE PROOF, Geometric and functional analysis, 8(2), 1998, pp. 234-242
Citations number
10
Categorie Soggetti
Mathematics,Mathematics
Journal title
Geometric and functional analysis → ACNP
ISSN journal
1016443X
Volume
8
Issue
2
Year of publication
1998
Pages
234 - 242
Database
ISI
SICI code
1016-443X(1998)8:2<234:OYAIC->2.0.ZU;2-#
Abstract
We give a new proof of the sharp form of Young's inequality for convol utions, first proved by Beckner [Be] and Brascamp-Lieb [BrLi]. The lat ter also proved a sharp reverse inequality in the case of exponents le ss than 1. Our proof is simpler and gives Young's inequality and its c onverse altogether.