- January 2015
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- We study functorial properties of the spaces R(X), which have been recently introduced as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space.. so that the equation R(X) = Lambda(phi) has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that f R(X) = Lambda(phi), then we can always take X to be the minimal r.i. Banach range space for the Hardy operator defined in Lambda(phi).