On reiteration between families of Banach spaces

Abstract

In this paper we briefly discuss some developments concerning real and complex interpolations between finite many or even between general families of Banach spaces. Moreover, we present and apply some reiteration theorem. In particular, we give an interpolation proof of a version of Hölder's inequality for families of $X^p$-spaces and a technique to characterize the interpolation spaces between some concrete families of Banach spaces. Some examples, open questions, and the relations to other connected results are pointed out.