On the norm of an integral operator and applications

被引：68
作者：
Yang, Bicheng [1 ]
机构：
[1] Guangdong Inst Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2006年 / 321卷 / 01期
关键词：
norm; integral operator; bilinear integral inequality; beta function; Hilbert's type inequality;
D O I：
10.1016/j.jmaa.2005.07.071
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the norm of an integral operator T : L-r (0, infinity) -> L-r (0, infinity) (r > 1) is obtained. As applications, a new bilinear integral operator inequality with the norm and the equivalent forms are given, and some new Hilbert's type inequalities with the best constant factors as the particular cases are established. (c) 2005 Elsevier Inc. All rights reserved.
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页码：182 / 192
页数：11
相关论文
共 10 条
  • [1] Hardy G.H., 1952, INEQUALITIES
  • [2] HARDY GH, 1925, P LONDON MATH SOC, V23
  • [3] Kuang J. C., 2003, APPL INEQUALITIES
  • [4] Mitrinovic DS, 1991, INEQUALITIES INVOLVI
  • [5] TAYLOR AE, 1976, INTRO FUNCTIONAL ANA
  • [6] WANG Z. X., 1979, Introduction to special functions
  • [7] Yang BC, 1998, J MATH ANAL APPL, V220, P778
  • [8] Yang BC, 2003, MATH INEQUAL APPL, V6, P625
  • [9] On the extended Hardy-Hilbert's inequality
    Yang, BC
    Debnath, L
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 272 (01) : 187 - 199
  • [10] A bilinear inequality
    Zhang, KW
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 271 (01) : 288 - 296
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