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.
引用
收藏
页码：2647 / 2656
页数：10
相关论文
共 50 条
  • [31] A note on the Cauchy-Schwarz inequality for expectations
    Farhadian, Reza
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2024, 53 (02) : 812 - 813
  • [32] THE CAUCHY-SCHWARZ INEQUALITY - A GEOMETRIC PROOF
    CANNON, JW
    AMERICAN MATHEMATICAL MONTHLY, 1989, 96 (07): : 630 - 631
  • [33] A CAUCHY-SCHWARZ INEQUALITY FOR OPERATORS WITH APPLICATIONS
    BHATIA, R
    DAVIS, C
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 224 : 119 - 129
  • [34] A CAUCHY-SCHWARZ INEQUALITY FOR TRIPLES OF VECTORS
    Arav, Marina
    Hall, Frank J.
    Li, Zhongshan
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2008, 11 (04): : 629 - 634
  • [35] ON A SPECIAL FORM OF THE CAUCHY-SCHWARZ INEQUALITY
    THIELE, L
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1985, 319 (04): : 405 - 412
  • [36] Cauchy-Schwarz inequality and particle entanglement
    Wasak, T.
    Szankowski, P.
    Zin, P.
    Trippenbach, M.
    Chwedenczuk, J.
    PHYSICAL REVIEW A, 2014, 90 (03):
  • [37] Remark on a refinement of the Cauchy-Schwarz inequality
    Zheng, L
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 218 (01) : 13 - 21
  • [38] Cauchy-Schwarz inequality and generalized Bernstein-type inequalities
    Lin, CS
    INEQUALITY THEORY AND APPLICATIONS, VOL 1, 2001, : 209 - 217
  • [39] Bell inequality for qubits based on the Cauchy-Schwarz inequality
    Chen, Jing-Ling
    Deng, Dong-Ling
    PHYSICAL REVIEW A, 2009, 79 (01):
  • [40] REFINEMENTS OF THE CAUCHY-SCHWARZ INEQUALITY FOR τ-MEASURABLE OPERATORS
    Han, Yazhou
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (04): : 919 - 931
12345