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Eurasian Mathematical Journal, 2017, Volume 8, Number 1, Pages 23–33 (Mi emj245)  

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
References:
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.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0008
8215.2016.1
Russian Foundation for Basic Research 15-01-02732_а
The publication was supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.A03.21.0008), by the grant of President of Russian Federation for support of Scientific Schools (Project no. 8215.2016.1), and by the grant of RFBR (Project no. 15-01-02732).
Received: 27.12.2016
Bibliographic databases:
Document Type: Article
MSC: 46E30, 42A16
Language: English
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
Citation in format AMSBIB
\Bibitem{BakGol17}
\by E.~G.~Bakhtigareeva, M.~L.~Goldman
\paper Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space
\jour Eurasian Math. J.
\yr 2017
\vol 8
\issue 1
\pages 23--33
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3663344}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000411744800002}
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