An Improvement of Hardy's Inequality for Hilbert Space Operators

被引：0

作者：

Kian, Mohsen ^{[1
]}

Delavar, Mohsen Rostamian ^{[1
]}

机构：

[1] Univ Bojnord, Fac Basic Sci, Dept Math, POB 1339, Bojnord 94531, Iran

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2019年 / 13卷 / 03期

关键词：

Hardy inequality; p-integrable; Weakly measurable mapping; Superquadratic function;

D O I：

10.1007/s11785-018-0846-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, using the notion of superquadratic functions and operator valued mappings, we give an improvement of the Hardy inequality for Hilbert space operators. Then we apply our results to the classical Hardy inequality. In particular, we obtain an estimation for the positive expression p p - 1 p 8 0 f ( x) pdx - 8 0 1 x x 0 f ( t) dt p dx, where p = 1 and f is a positive p- integrable function on (0,infinity).

引用

页码：1133 / 1141

页数：9

共 14 条

[1]

Abramovich S., 2004, Bull. Math. Sc. Math. Roum, V47, P3

[2]

[Anonymous], 1967, INEQUALITIES

[3] Hardy type inequaltiy for reproducing Kernel Hilbert space operators and related problems [J].

Garayev, Mubariz T. ;

Gurdal, Mehmet ;

Saltan, Suna .

POSITIVITY, 2017, 21 (04) :1615-1623

[4] HARDY-HILBERT'S INEQUALITY AND POWER INEQUALITIES FOR BEREZIN NUMBERS OF OPERATORS [J].

Garayev, Mubariz T. ;

Gurdal, Mehmet ;

Okudan, Arzu .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2016, 19 (03) :883-891

[5] Non-commutative Hardy inequalities [J].

Hansen, Frank .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 :1009-1016

[6]

HARDY G. H., 1925, MESSENGER MATH, V54, P150, DOI DOI 10.1007/BF01199965.[

[7] Note on a theorem of Hilbert. [J].

Hardy, GH .

MATHEMATISCHE ZEITSCHRIFT, 1920, 6 :314-317

[8] On a Hardy operator inequality [J].

Kian, Mohsen .

POSITIVITY, 2018, 22 (03) :773-781

[9] Inequalities Involving Superquadratic Functions and Operators [J].

Kian, Mohsen ;

Dragomir, S. S. .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2014, 11 (04) :1205-1214

[10] Operator Jensen inequality for superquadratic functions [J].

Kian, Mohsen .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 456 :82-87

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