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No abstract

Abstract. Let p ∈ (0, ∞) , let v be a weight on (0, ∞) and let Λ p (v) be the classical Lorentz space, determined by the norm

We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a δ-ring. A precise description is given for the case of the minimal Lorentz spaces.

We apply the expression for the norm of a function in the weighted Lorentz space, with respect to the distribution function, to obtain as a simple consequence some weighted inequalities for integral operators.