Singular integral operators on tent spaces: a Calderón–Zygmund theory and weak-type endpoint estimates

We propose a Calderón–Zygmund-type extrapolation theory for sublinear operators acting on the so-called tent spaces introduced by Coifman et al. (J Funct Anal 62(2):304–335, 1985). As an application, we prove endpoint weak-type estimates for the article [referred to as Auscher et al. (J Evol Equ 12(4):741–765, 2012)]. The main ingredient in establishing this extrapolation theory is the use of some Calderón–Zygmund-type decompositions in tent spaces. In applying this abstract theory to the class of singular integral operators on tent spaces as considered in [3], we shall use certain Hardy–Littlewood embeddings for tent space functions. These embeddings are also interesting in themselves. Applications to maximal regularity operators on tent spaces are also discussed.