Abstract:
In this paper we obtain estimates for the integrals of monotone functions arising in the study of the covering
of various cones of functions with monotonicity conditions. We apply the method of covering of the cones
with the help of generalized Hardy operator. Sharp conditions are found on the kernels of representations for
the validity of given estimates on the cones. The proofs are based on the reduction of integral estimates on
the cones of monotone functions to ones on the family of characteristic functions of intervals. The obtained
results can be used in finding the condition for the mutual covering of cones associated with decreasing
rearrangement of the generalized Bessel and Riesz potentials.
