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

被引：66

作者：

Barthe, F ^{[1
]}

机构：

[1] Univ Marne la Vallee, Equipe Anal & Math Appl, F-77454 Marne La Vallee 2, France

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 1998年 / 8卷 / 02期

关键词：

Simple Proof; Reverse Inequality; Sharp Form;

D O I：

10.1007/s000390050054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：234 / 242

页数：9

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