Nikishin’s theorem and factorization through Marcinkiewicz spaces
Copyright policy )Nikishin’s theorem and factorization through Marcinkiewicz spaces
Consider L 0 L^0 , the F 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 L^0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 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.
Nikishin theorem, Rademacher type and cotype, Marcinkiewicz space, Orlicz space, Spaces of operators; tensor products; approximation properties, Lipschitz operator, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Nikishin theorem, Rademacher type and cotype, Marcinkiewicz space, Orlicz space, Spaces of operators; tensor products; approximation properties, Lipschitz operator, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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