Nikishin s theorem, Orlicz type and factorization through Marcinkiewicz spaces

Abstract

[EN] Consider L 0 , the F-space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin's classical result on the factorization of sublinear continuous operators from a Banach space to L 0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.