Abstract
A monotone operator P mapping the Orlicz–Lorentz class to an ideal space is considered. The Orlicz–Lorentz class is the cone of measurable functions on R + =(0, ∞) whose decreasing rearrangements with respect to the Lebesgue measure on R + belong to the weighted Orlicz space L Φ,ν. Reduction theorems are proved, which make it possible to reduce estimates of the norm of the operator P: ΛΦ,ν →Y to those of the norm of its restriction to the cone of nonnegative step functions in L Φ,ν. The application of these results to the identity operator from ΛΦ,ν to the weighted Lebesgue space Y = L 1(R +; g) gives exact descriptions of associated norms for ΛΦ,ν.
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Original Russian Text © M.L. Goldman, 2016, published in Doklady Akademii Nauk, 2016, Vol. 471, No. 2, pp. 131–135.
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Goldman, M.L. Estimates for the norms of monotone operators on weighted Orlicz–Lorentz classes. Dokl. Math. 94, 627–631 (2016). https://doi.org/10.1134/S1064562416060065
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DOI: https://doi.org/10.1134/S1064562416060065