Maximal functions, factorization, and the R-boundedness of integral operators

We generalize a recent result on the ℓs-boundedness of a family of integral operators from the weighted vector-valued Lp(Rd,w;Lq(Ω)) setting to the weighted vector-valued Lp(Rd,w;X) setting for a large class of Banach function spaces X. For this we first extensively study the first part of an unpublished manuscript on the factorization of ℓ2...