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

被引：10

作者：

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

Shambilova, G. E. ^{[3
]}

Stepanov, V. D. ^{[3
,4
]}

机构：

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

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

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

[4] Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2015年 / 9卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Hardy-type inequality; weight; measure; Lorentz space; concave function; quasi-concave function; LORENTZ SPACES;

D O I：

10.15352/bjma/09-2-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The complete characterization of the Hardy-type L-p-L-q inequalities on the weighted cones of quasi-concave functions for all 0 < p, q < infinity is given.

引用

页码：21 / 34

页数：14

共 16 条

[1] 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

[2]

Bennett C., 1988, INTERPOLATION OPERAT

[3]

Carro MJ, 2007, MEM AM MATH SOC, V187, pIX

[4] 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

[5] Some New Iterated Hardy-Type Inequalities [J].

Gogatishvili, A. ;

Mustafayev, R. Ch ;

Persson, L-E .

JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2012,

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

Gogatishvili, A ;

Pick, L .

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

[7] Some new iterated Hardy-type inequalities: the case θ=1 [J].

Gogatishvili, Amiran ;

Mustafayev, Rza ;

Persson, Lars-Erik .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,

[8]

Goldman ML, 2005, DOKL MATH, V71, P209

[9] On the principle of duality in Lorentz spaces [J].

GolDman, ML ;

Heinig, HP ;

Stepanov, VD .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1996, 48 (05) :959-979

[10]

Kantorovich L. V., 1982, Functional analysis, V2nd

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