Tent spaces of vector-valued functions were recently studied by Hyt\"onen,
van Neerven and Portal with an eye on applications to H^\infty-functional
calculi. This paper extends their results to the endpoint cases p = 1 and p =
\infty along the lines of earlier work by Harboure, Torrea and Viviani in the
scalar-valued case. The main result of the paper is an atomic decomposition in
the case p = 1, which relies on a new geometric argument for cones. A result on
the duality of these spaces is also given.Comment: 19 pages, minor corrections mad