Modular and norm inequalities for operators on the cone of decreasing functions in Orlicz space - Bakhtigareeva, Elza Gizarovna; Goldman, Michail L’vovich (Eurasian Mathematical Journal, 2017)
Modular and norm inequalities are considered on the cone of all nonnegative functions as well as on the cone \( Ω \) of all nonnegative decreasing functions in the weighted Orlicz space. Reduction theorems are proved for the norm of positively homogeneous operator on the cone \( Ω \). 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.