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Spring 2009 Hardy spaces of operator-valued analytic functions
Zeqian Chen
Illinois J. Math. 53(1): 303-324 (Spring 2009). DOI: 10.1215/ijm/1264170852

Abstract

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of $\mathbb{C}$. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operator-valued $\mathrm{H}^1$-BMOA duality theorem is proved. Finally, by the $\mathrm{H}^1$-BMOA duality we present the Lusin area integral and Littlewood-Paley $g$-function characterizations of the operator-valued analytic Hardy space.

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Zeqian Chen. "Hardy spaces of operator-valued analytic functions." Illinois J. Math. 53 (1) 303 - 324, Spring 2009. https://doi.org/10.1215/ijm/1264170852

Information

Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1197.46033
MathSciNet: MR2584948
Digital Object Identifier: 10.1215/ijm/1264170852

Subjects:
Primary: 32A37 , 46E40

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 1 • Spring 2009
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