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.
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Original Russian Text © M. L. Goldman, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 1, pp. 30–46.
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Goldman, M.L. Estimates for restrictions of monotone operators on the cone of decreasing functions in Orlicz space. Math Notes 100, 24–37 (2016). https://doi.org/10.1134/S0001434616070038
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DOI: https://doi.org/10.1134/S0001434616070038