Lipschitz (q, p)-Summing Maps from C(K)-Spaces to Metric Spaces

Abstract

AbstractVariants of the notion of (q, p)-summing operator are introduced in the setting of Lipschitz mappings acting between metric spaces. Some classes of these operators from C(K)-spaces to metric spaces are studied. An integral domination estimate is proved for a class of the mentioned Lipschitz (q, p)-summing maps. It is shown that under some conditions this domination is equivalent to (q, 1)-summability of these Lipschitz maps. As an application, we recover Pisier’s result, which provides this equivalence in the setting of the linear operators.