This is an announcement for the paper "On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators" by Mikko Kemppainen.
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).
Archive classification: math.FA
Mathematics Subject Classification: 42B35 (Primary), 46E40 (Secondary)
Remarks: 19 pages
Submitted from: mikko.k.kemppainen@helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2886
or