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Artículo
Orlicz spaces associated to a quasi‑Banach function space: applications to vector measures and interpolation
(Springer, 2021)
The Orlicz spaces XΦ associated to a quasi-Banach function space X are defined by replacing the role of the space L1 by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this ...
Artículo
Complex Interpolation of Operators and Optimal Domains
(Springer, 2014)
Let X0 and X1 be two order continuous Banach function spaces on a finite measure space, (E0, E1) a Banach space interpolation pair, and T : X0 + X1 → E0 + E1 an admissible operator between the pairs (X0, X1) and (E0, ...
Artículo
Compactness in quasi-Banach function spaces with applications to L1 of the semivariation of a vector measure
(Springer, 2020)
We characterize the relatively compact subsets of the order continuous part Ea of a quasi Banach function space E showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, ...
Artículo
When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?
(Elsevier, 2020)
We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context of the generalized Orlicz spaces associated to an N-function Φ and a (quasi-) Banach function space X over a positive finite measure ...
Artículo
Lorentz spaces of vector measures and real interpolation of operators
(Taylor and Francis, 2020)
Using the representation of the real interpolation of spaces of p-integrable functions with respect to a vector measure, we show new factorization theorems for p th power factorable operators acting in interpolation couples ...
Artículo
Interpolation of Vector Measures
(Springer, 2011)
Let (Ω, Σ) be a measurable space and m 0: Σ → X 0 and m 1: Σ → X 1 be positive vector measures with values in the Banach Köthe function spaces X 0 and X 1. If 0 < α < 1, we define a new vector measure [m 0, m 1] α with ...
Artículo
The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure
(Elsevier, 2019)
For a vector measure m, with values in a Banach space, we analyze the localization of uniformly integrable subsets of scalar integrable functions with respect to m in a suitable Orlicz space associated to m. As tools we ...
Artículo
A note on real interpolation of L-P-spaces of vector measures on delta-rings
(Elsevier, 2014)
We describe the real interpolation spaces obtained when we apply the real K-method of Lions–Peetre to Banach lattices of p-integrable and weakly p-integrable functions with respect to a Banach-space-valued measure defined ...
Artículo
Weighted Hardy inequalities, real interpolation methods and vector measures
(Springer, 2014)
We analyze the relationship of the Ariño–Muckenhoupt weights with the K - spaces obtained when the real interpolation method defined by a parameter function is applied to the pairs (L 1 , L∞) and (L 1,∞, L∞) of function ...
Artículo
Complex interpolation of L-p-spaces of vector measures on delta-rings
(Elsevier, 2013)
We apply the Calderón interpolation methods to Banach lattices of p-integrable and weakly p-integrable functions with respect to a Banach-space-valued measure defined on a δ-ring. In general, the results we obtain are ...