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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Submitted: March 1997, Final version: April 1997
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Barthe, F. Optimal young's inequality and its converse: a simple proof. GAFA, Geom. funct. anal. 8, 234–242 (1998). https://doi.org/10.1007/s000390050054
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DOI: https://doi.org/10.1007/s000390050054