Hardy-type Inequalities on Cones of Monotone Functions

Abstract: This Licentiate thesis deals with Hardy-type inequalities restricted to cones of monotone functions. The thesis consists of two papers (paper A and paper B) and an introduction which gives an overview to this specific field of functional analysis and also serves to put the papers into a more general frame. We deal with positive σ-finite Borel measures on R_+:=[0,∞) and the class M↓(M↑) consisting of all non-increasing (non-decreasing) Borel functions f∶ R_+→[0,+∞ ]. In paper A some two-sided inequalities for Hardy operators on the cones of monotone functions are proved. In the paper some equivalences are found for some the Hardy-type operators for the full range of parameter p,p≠0. As an application of one of the results, we also obtain a new characterization of the discrete inequality for one of the most interesting cases of parameters, namely when 0