Boza, SantiagoSoria de Diego, Francisco Javier2024-01-172024-01-172019S. Boza, J. Soria, Averaging operators on decreasing or positive functions: Equivalence and optimal bounds, Journal of Approximation Theory 237 (2019) 135–152. https://doi.org/10.1016/j.jat.2018.09.001.0021-904510.1016/j.jat.2018.09.001https://hdl.handle.net/20.500.14352/93658We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S∗, on the full range 1 ≤ p ≤ ∞, for the cases of decreasing, positive or general functions (in fact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1 < p ≤ 2, we prove that all these estimates are the same, but for 2 < p < ∞, they exhibit a completely different behavior.engjournal articlehttps://doi.org/10.1016/j.jat.2018.09.001https://www.sciencedirect.com/science/article/pii/S0021904518301023open accessHardy operatorDual operatorBests constantsDecreasing functionsCiencias12 Matemáticas