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

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

• The Orlicz spaces X^{\varPhi } associated to a quasi-Banach function space X are defined by replacing the role of the space L^1 by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces L^1_w(m), L^1(m) and L^1(\Vert m\Vert ) of integrable functions (in the weak, strong and Choquet sense, respectively) in order to obtain the known Orlicz spaces L^{\varPhi }_w(m) and L^{\varPhi }(m) and the new ones L^{\varPhi }(\Vert m\Vert ). 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.