Weighted inequalities involving iteration of two Hardy integral operators

Abstract

f (x)dx, for all non-negative measurable functions on (a, b), −∞ ≤ a < b ≤ ∞. We construct a more straightforward discretization method than those previously presented in the literature, and we characterize this inequality in both discrete and continuous forms.2010 Mathematics Subject Classification. 26D10. Key words and phrases. weighted Hardy inequality, iterated operators, Copson operator, Hardy operator, inequalities for monotone functions. Recently,in [4], with a new and simpler discretization technique requires neither parameter restrictions nor non-degeneracy conditions, characterization of (1.1) is given. We adapt this approach to the specific demands of the inequality considered in this paper.

New equivalence theorems for weighted inequalities involving the composition of monotone quasilinear operators with the Hardy and Copson operators and their applications

“…The "classical" conditions ensuring the validity of (4.9) was recently presented in [26]. Inequalities (4.8) and (4.10) were recently characterized by using discretization techniques in [13] and [24], respectively. The characterization of inequality (4.8) by using a combination of reduction techniques and discretization was lately presented in [32].…”

Another approach to weighted inequalities for a superposition of Copson and Hardy operators

“…The "classical" conditions ensuring the validity of (1.3) was recently presented in [19]. Inequalities (1.2) and (1.4) were recently characterized by using discretization techniques in [6] and [17], respectively.…”