Geodesic
Weighted Inequalities for Hardy-Type Operators
Matematičeskie zametki, Tome 102 (2017) no. 5, pp. 673-683.

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We establish criteria for the validity of modular inequalities for the Hardy operator on the cone $\Omega$ of nonnegative decreasing functions from weighted Orlicz spaces with general weight. The result is based on the theorem on the reduction of modular inequalities for positively homogeneous operators on the cone $\Omega$, which enables passing to modular inequalities for modified operators on the cone of all nonnegative functions from an Orlicz space. It is shown that, for the Hardy operator, the modified operator is a generalized Hardy operator. This enables us to establish explicit criteria for the validity of modular inequalities.
Keywords: Hardy operator, generalized Hardy operator, cone of decreasing functions, weighted Orlicz space, modular inequality. 
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E. G. Bakhtigareeva; M. L. Gol'dman. Weighted Inequalities for Hardy-Type Operators. Matematičeskie zametki, Tome 102 (2017) no. 5, pp. 673-683. http://geodesic.mathdoc.fr/item/MZM_2017_102_5_a3/

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