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ON VECTOR-VALUED TENT SPACES AND HARDY SPACES ASSOCIATED WITH NON-NEGATIVE SELF-ADJOINT OPERATORS

Part of: Linear function spaces and their duals Harmonic analysis in several variables

Published online by Cambridge University Press:  21 July 2015

MIKKO KEMPPAINEN
MIKKO KEMPPAINEN*
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
*
Current address: Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki, Finland e-mail: mikko.k.kemppainen@helsinki.fi
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Abstract

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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 H1L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T1(X).

MSC classification

Primary: 42B35: Function spaces arising in harmonic analysis
Secondary: 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 689 - 716
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

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