Estimates for the norms of integral and discrete operators of Hardy type on cones of quasimonotone functions

The author claims a number of results concerning boundedness of Hardy-type operators such as (int_{0}^{t}fsp r,dmu)^{1/r} or (int_{t}^{infty}fsp r,dmu)^{1/r}, t>0, in quite a general setting on cones of functions with certain monotonicity properties; namely, the cones Omega_k of functions fgeq0 such that f/k is decreasing and Omega^{m} of functions fgeq0 such that f/m is increasing, where k,m are fixed functions on (0,infty). The results generalize earlier work of the author. Discrete versions are treated, too. Proofs are not included.