INEQUALITIES FOR OPERATORS ON THE CONE OF DECREASING FUNCTIONS IN WEIGHTED ORLICZ SPACE

Norm inequalities are considered on the cone of nonnegative functions as well as on the cone Ω of nonnegative decreasing functions in the weighted Orlicz space. The reduction theorems are presented for the norm of positively homogeneous operator on the cone Ω. It is equivalent to the norm of some modified operator on the cone of all nonnegative functions in this space.