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

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

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 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).

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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