, Volume 8, Issue 2, pp 234-242

Optimal young's inequality and its converse: a simple proof

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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.

Submitted: March 1997, Final version: April 1997