On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators

Abstract

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X).

20 pages, references added, revised, to appear in Glasgow Mathematical Journal

References in corpus (2)

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

Cited by in corpus (2)

• Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces
• Best constants in the vector-valued Littlewood-Paley-Stein theory