Geodesic
Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space
Eurasian mathematical journal, Tome 8 (2017) no. 1, pp. 23-33

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Modular and norm inequalities are considered on the cone of all nonnegative functions as well as on the cone $\Omega$ of all nonnegative decreasing functions in the weighted Orlicz space. Reduction theorems are proved for the norm of positively homogeneous operator on the cone $\Omega$. We show that it is equivalent to the norm of a certain modified operator on the cone of all nonnegative functions in this space. Analogous results are established for modular inequalities. 
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     author = {E. G. Bakhtigareeva and M. L. Goldman},
     title = {Modular and norm inequalities for operators on the cone of decreasing functions in {Orlicz} space},
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E. G. Bakhtigareeva; M. L. Goldman. Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space. Eurasian mathematical journal, Tome 8 (2017) no. 1, pp. 23-33. http://geodesic.mathdoc.fr/item/EMJ_2017_8_1_a2/