Geodesic
Estimates for Restrictions of Monotone Operators on the Cone of Decreasing Functions in Orlicz Space
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 30-46.

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The restriction of a monotone operator $P$ to the cone $\Omega$ of nonnegative decreasing functions from a weighted Orlicz space $L_{\varphi,v}$ without additional a priori assumptions on the properties of the Orlicz function $\varphi$ and the weight function $v$ is considered. An order-sharp two-sided estimate of the norm of this restriction is established by using a specially constructed discretization procedure. Similar estimates are also obtained for monotone operators over the corresponding Orlicz–Lorentz spaces $\Lambda_{\varphi,v}$. As applications, descriptions of associated spaces for the cone $\Omega$ and the Orlicz–Lorentz space are obtained. These new results are of current interest in the theory of such spaces.
Keywords: monotone operator, weighted Orlicz space, cone of decreasing functions, associated norm, Orlicz–Lorentz class, discretization method. 
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M. L. Gol'dman. Estimates for Restrictions of Monotone Operators on the Cone of Decreasing Functions in Orlicz Space. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 30-46. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a2/

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