Illinois Journal of Mathematics

Hardy spaces of operator-valued analytic functions

Zeqian Chen

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

First available in Project Euclid: 22 January 2010

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Zentralblatt MATH identifier

Primary: 46E40: Spaces of vector- and operator-valued functions 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]


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

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