WEIGHTED HARDY-TYPE INEQUALITIES ON THE CONE OF QUASI-CONCAVE FUNCTIONS

被引：5

作者：

Persson, L. -E. ^{[1
,2
]}

Popova, O. V. ^{[3
]}

Stepanov, V. D. ^{[3
]}

机构：

[1] Lulea Univ Technol, Dept Engn Sci & Math, SE-97187 Lulea, Sweden

[2] Narvik Univ, NO-8505 Narvik, Norway

[3] Peoples Friendship Univ Russia, Dept Math Anal & Funct Theory, Moscow 117198, Russia

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2014年 / 17卷 / 03期

关键词：

Hardy operator; Hardy-type inequality; weight; measure; Lorentz space; concave function; quasi-concave function; REDUCTION THEOREMS; MONOTONE; OPERATORS; EMBEDDINGS;

D O I：

10.7153/mia-17-64

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is devoted to the study of weighted Hardy- type inequalities on the cone of quasi- concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz Gamma- spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters q >= 1, p > 0 and sufficient conditions for the rest of the range of parameters.

引用

页码：879 / 898

页数：20

共 33 条

[1]

[Anonymous], 1976, GRUNDLEHREN MATH WIS

[2] MAXIMAL FUNCTIONS ON CLASSICAL LORENTZ SPACES AND HARDY INEQUALITY WITH WEIGHTS FOR NONINCREASING FUNCTIONS [J].

ARINO, MA ;

MUCKENHOUPT, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 320 (02) :727-735

[3]

Asekritova IU, 1997, STUD MATH, V124, P107

[4]

Bennett C., 1988, Interpolation of operators

[5] Weighted Hardy inequalities for decreasing sequences and functions [J].

Bennett, G ;

Grosse-Erdmann, KG .

MATHEMATISCHE ANNALEN, 2006, 334 (03) :489-531

[6] On embeddings between classical Lorentz spaces [J].

Carro, M ;

Pick, L ;

Soria, J ;

Stepanov, VD .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2001, 4 (03) :397-428

[7]

Carro M, 2008, J OPERAT THEOR, V59, P309

[8] Reduction theorems for weighted integral inequalities on the cone of monotone functions [J].

Gogatishvili, A. ;

Stepanov, V. D. .

RUSSIAN MATHEMATICAL SURVEYS, 2013, 68 (04) :597-664

[9] Operators on cones of monotone functions [J].

Gogatishvili, A. ;

Stepanov, V. D. .

DOKLADY MATHEMATICS, 2012, 86 (01) :562-565

[10] Discretization and anti-discretization of rearrangement-invariant norms [J].

Gogatishvili, A ;

Pick, L .

PUBLICACIONS MATEMATIQUES, 2003, 47 (02) :311-358

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