A Cauchy-Schwarz type inequality for bilinear integrals on positive measures

被引：12
|
作者：
Ackermann, N [1 ]
机构：
[1] Univ Giessen, Math Inst, D-35392 Giessen, Germany
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 133卷 / 09期
关键词：
integral inequalities; positive definite functions; Cauchy-Schwarz inequality;
D O I：
10.1090/S0002-9939-05-08082-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
If . : R-n -> [0.infinity] is Borel measurable, define for .-finite positive Borel measures ... on R-n the bilinear integral expression .(. ; ...) := integral(R)(n) integral(R)(n) .(. - .) .. (.) .. (.). We give conditions on (.) such that there is a constant (.) >= 0, independent of (.) and ., with .(. ; ...) <= root.(.(. ; ...) . (. ; ...). Our results apply to a much larger class of functions (.) than known before.
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页码：2647 / 2656
页数：10
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