The vector-valued tent spaces T^1 and T^\infty

Abstract

Tent spaces of vector-valued functions were recently studied by Hytönen, 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.

19 pages, minor corrections made

References in corpus (1)

• Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi

Cited by in corpus (2)

• On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators
• Best constants in the vector-valued Littlewood-Paley-Stein theory