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

Details Optimal Young's inequality and its converse:a simple proof Optimal Young's inequality and its converse:a simple proof

1997-04-05

arxiv.org/abs/math/9704210v1

Mathematics

Functional Analysis

Scientific paper

We give a new proof of the sharp form of Young's inequality for
convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. 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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