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

The restriction of a monotone operator P to the cone Omega of nonnegative decreasing functions from a weighted Orlicz space L (phi,v) without additional a priori assumptions on the properties of theOrlicz function phi 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 I > (phi,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.