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THE VECTOR-VALUED TENT SPACES $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}T^1$ AND $T^{\infty }$

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  15 May 2014

MIKKO KEMPPAINEN
MIKKO KEMPPAINEN*
Affiliation:
Department of Mathematics and Statistics,University of Helsinki, Gustaf Hällströmin katu 2b, FI-00014 Helsinki, Finland email mikko.k.kemppainen@helsinki.fi
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Abstract

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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.

Keywords

vector-valued harmonic analysisatomic decompositionstochastic integration

MSC classification

Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 1 , August 2014 , pp. 107 - 126
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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