Hardy spaces of operator-valued analytic functions

Details Hardy spaces of operator-valued analytic functions Hardy spaces of operator-valued analytic functions

2008-08-10

arxiv.org/abs/0808.1387v2

Illinois J.Math. vol.53, 303-324(2009)

Mathematics

Functional Analysis

22 pages

Scientific paper

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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