Inequalities for Hardy-type operators on the cone of decreasing functions in a weighted Orlicz space

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. © 2017, Pleiades Publishing, Ltd.

Number of issue
3
Language
English
Pages
553-557
Status
Published
Volume
96
Year
2017
Organizations
  • 1 RUDN University, Moscow, 117198, Russian Federation
  • 2 Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russian Federation
Date of creation
19.10.2018
Date of change
17.03.2021
Short link
https://repository.rudn.ru/en/records/article/record/5227/
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