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Averaging operators on decreasing or positive functions: Equivalence and optimal bounds Boza, Santiago Soria de Diego, Francisco Javier Hardy operator Dual operator Bests constants Decreasing functions Ciencias 12 Matemáticas 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. Ministerio de Economía, Comercio y Empresa (España) Generalitat de Catalunya Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2024-01-17T16:05:01Z 2024-01-17T16:05:01Z 2019 journal article AM https://hdl.handle.net/20.500.14352/93658 0021-9045 10.1016/j.jat.2018.09.001 eng MTM2016-75196-P 2017SGR358 S. 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. open access application/pdf Elsevier