GENERALIZED NONCOMMUTATIVE HARDY AND HARDY-HILBERT TYPE INEQUALITIES

被引：9

作者：

Hansen, Frank ^{[1
]}

Krulic, Kristina ^{[2
]}

Pecarici, Josip ^{[2
]}

Persson, Lars-Erik ^{[3
]}

机构：

[1] Univ Copenhagen, Dept Econ, DK-1353 Copenhagen, Denmark

[2] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

[3] Lulea Univ Technol, Dept Math, SE-97187 Lulea, Sweden

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2010年 / 21卷 / 10期

关键词：

Inequalities; Hardy's inequality; Hardy-Hilbert's inequality; Godunova's inequality; weights; positive operator; operator convex functions;

D O I：

10.1142/S0129167X10006501

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p <= 2, even for functions with values in 2 x 2 matrices.

引用

页码：1283 / 1295

页数：13

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