Reduction theorems for operators on the cones of monotone functions

被引：23

作者：

Gogatishvili, Amiran ^{[1
]}

Stepanov, Vladimir D. ^{[2
]}

机构：

[1] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Peoples Friendship Univ Russia, Moscow 117198, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 405卷 / 01期

关键词：

Quasilinear operator; Integral inequality; Lebesgue space; Weight; Hardy operator; Monotone functions; CLASSICAL LORENTZ SPACES; WEIGHTED HARDY INEQUALITIES; INTEGRAL-OPERATORS; NONINCREASING FUNCTIONS; EMBEDDINGS; BOUNDEDNESS;

D O I：

10.1016/j.jmaa.2013.03.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in the L-p - L-q setting for 0 < q < infinity, 1 < p < infinity. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain criteria for three-weight inequalities for the Hardy-type operators on monotone functions in the case 0 < q < p <= 1. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：156 / 172

页数：17

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