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
收藏
页码：156 / 172
页数：17
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