Optimal young's inequality and its converse: a simple proof
Optimal young's inequality and its converse: a simple proof
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DOI：
10.1007/s000390050054
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发表时间：
1997-04
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影响因子：
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通讯作者：
F. Barthe
中科院分区：
文献类型：
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作者：
F. Barthe
首先由Beckner [Be]和Brascamp-Lieb [BrLi]证明的关于卷积的杨氏不等式的尖锐形式给出了一个新的证明。后者在指数小于1的情况下也证明了一个尖锐的反向不等式。我们的证明更简单，并给出了杨氏不等式及其逆。
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.