Estimates for restrictions of monotone operators on the cone of decreasing functions in Orlicz space

Abstract

The restriction of a monotone operator P to the cone Ω of nonnegative decreasing functions from a weighted Orlicz space L_φ,v without additional a priori assumptions on the properties of theOrlicz function φ 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 Λ_φ,v. As applications, descriptions of associated spaces for the cone Ω and the Orlicz–Lorentz space are obtained. These new results are of current interest in the theory of such spaces.