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. 
@article{MZM_2016_100_1_a2,
     author = {M. L. Gol'dman},
     title = {Estimates for {Restrictions} of {Monotone} {Operators} on the {Cone} of {Decreasing} {Functions} in {Orlicz} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {30--46},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a2/}
}
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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/