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Eurasian Mathematical Journal, 2017, Volume 8, Number 1, Pages 23–33
(Mi emj245)
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Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space
E. G. Bakhtigareeva, M. L. Goldman Department of Nonlinear Analysis and Optimization,
Peoples' Friendship University of Russia (RUDN University),
6 Mikluho-Maklaya St.,
117198 Moscow, Russian Federation
Abstract:
Modular and norm inequalities are considered on the cone of all nonnegative functions as well as on the cone $\Omega$ of all nonnegative decreasing functions in the weighted Orlicz space. Reduction theorems are proved for the norm of positively homogeneous operator on the cone $\Omega$. We show that it is equivalent to the norm of a certain modified operator on the cone of all nonnegative functions in this space. Analogous results are established for modular inequalities.
Keywords and phrases:
weighted Orlicz spaces, modular and norm inequalities, cone of decreasing functions, reduction theorems.
Received: 27.12.2016
Citation:
E. G. Bakhtigareeva, M. L. Goldman, “Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space”, Eurasian Math. J., 8:1 (2017), 23–33
Linking options:
https://www.mathnet.ru/eng/emj245 https://www.mathnet.ru/eng/emj/v8/i1/p23
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Abstract page: | 3426 | Full-text PDF : | 113 | References: | 47 |
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