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Resumen de Orlicz spaces associated to a quasi-Banach function space: applications to vector measures and interpolation

Ricardo del Campo Acosta Árbol académico, Antonio Fernández Carrión Árbol académico, Fernando Mayoral, Francisco Naranjo Naranjo Árbol académico

  • 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 construction to the spaces L1w(m), L1(m) and L1(∥m∥) of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces LΦw(m) and LΦ(m) and the new ones LΦ(∥m∥). Therefore, we are providing a framework where dealing with different kind of Orlicz spaces in a unified way. Some applications to complex interpolation are also given.


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