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Norm inequalities are considered on the cone of nonnegative functions as well as on the cone Ω

or optimal Banach function space, containing the given cone of nonnegative, decreasing functions in a

or optimal Banach function space, containing the given cone of nonnegative, decreasing functions in a

Optimal Banach function space for the given cone of decreasing functions from weighted Lp-space

of positive functions and on the cone of positive decreasing functions with common weight and common Young

of the covering of various cones of functions with monotonicity conditions. We apply the method of covering

through decreasing rearrangements of kernels and functions to be convolved. These estimates show

of nonnegative decreasing functions from weighted Orlicz spaces with general weight. The result is based

The restriction of a monotone operator P to the cone Ω of nonnegative decreasing functions from a

for monotone operators on the cones of functions with monotonicity properties. We implement a general approach

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