A vector-valued approach to tent spaces

In this paper we present a new point of view to study the tent spaces introduced by Coifman, Meyer and Stein ([CMS1] and [CMS2]) by immersing them into vector-valued Lebesgue, Hardy and BMO spaces. This approach allows us to derive many of the known properties for tent spaces in a very simple manner. In fact most of the results are obtained as a consequence of similar results for those vector-valued spaces where they are immersed. The main tool we use to obtain such immersions and the applications to boundedness of operators, given in &4, is the vector-valued Calderón-Zygmund theory.