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- Title
Inequalities for Hardy-type operators on the cone of decreasing functions in a weighted Orlicz space.
- Authors
Bakhtigareeva, E.; Gol'dman, M.
- Abstract
Modular inequalities and inequalities for the norms of Hardy-type operators on the cone Ω of positive functions and on the cone of positive decreasing functions with common weight and common Young function in a weighted Orlicz space are considered. A reduction theorem for the norm of the Hardy operator on the cone Ω is obtained. It is shown that this norm is equivalent to the norm of a modified operator on the cone of all positive functions in the space under consideration. It is proved that the modified operator is a generalized Hardy-type operator. The equivalence of modular inequalities on the cone Ω and modified modular inequalities on the cone of all positive functions in the Orlicz space is shown. A criterion for the validity of such inequalities in general Orlicz spaces is obtained and refined for weighted Lebesgue spaces.
- Subjects
ORLICZ lattices; HARDY spaces; MATHEMATICAL inequalities; RADON integrals; MATHEMATICAL formulas
- Publication
Doklady Mathematics, 2017, Vol 96, Issue 3, p553
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562417060059