%0 Journal Article
%A Boza, Santiago 
%A Soria de Diego, Francisco Javier
%T Averaging operators on decreasing or positive functions: Equivalence and optimal bounds
%D 2019
%@ 0021-9045
%U https://hdl.handle.net/20.500.14352/93658
%X We 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.
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