A Cauchy-Schwarz type inequality for bilinear integrals on positive measures期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Nils Ackermann

Affiliation:	Justus-Liebig-Universität, Mathematisches Institut, Arndtstr. 2, D-35392 Giessen, Germany

Abstract:	If $Wcolonmathbb{R} ^n to[0,infty]$ is Borel measurable, define for -finite positive Borel measures on $mathbb{R} ^n$ the bilinear integral expression $begin{displaymath}I(W;mu,nu):=int_{mathbb{R} ^n}int_{mathbb{R} ^n}W(x-y),dmu(x),dnu(y);. end{displaymath}$ We give conditions on such that there is a constant , independent of and , with Our results apply to a much larger class of functions than known before.

Keywords:	Integral inequalities positive definite functions Cauchy-Schwarz inequality

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