## Illinois Journal of Mathematics

### Hardy spaces of operator-valued analytic functions

Zeqian Chen

#### 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.

#### Article information

Source
Illinois J. Math., Volume 53, Number 1 (2009), 303-324.

Dates
First available in Project Euclid: 22 January 2010

https://projecteuclid.org/euclid.ijm/1264170852

Digital Object Identifier
doi:10.1215/ijm/1264170852

Mathematical Reviews number (MathSciNet)
MR2584948

Zentralblatt MATH identifier
1197.46033

#### Citation

Chen, Zeqian. Hardy spaces of operator-valued analytic functions. Illinois J. Math. 53 (2009), no. 1, 303--324. doi:10.1215/ijm/1264170852. https://projecteuclid.org/euclid.ijm/1264170852

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