(p,σ)-Absolutely Lipschitz operators

Abstract

Due to recent advances in the theory of ideals of Lipschitz mappings, we introduce $(p,\sigma )$-absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz absolutely $p$-summing mappings. Among other results, we prove a factorization theorem that provides a reformulation to the one given by Farmer and Johnson for Lipschitz absolutely $p$-summing mappings.