Duality of certain Banach spaces of vector-valued holomorphic functions
Abstract
In this work we study the vector-valued Hardy spaces H p (D; F) (1 ≤ p ≤ ∞) and their relationship with RNP, ARNP and the UMDP properties. By following the approach of Taylor in the scalar-valued case, we prove that, when F and F have the ARNP property, then H p (D; F) and H q (D; F) are canonically topologically isomorphic (for p, q ∈ (1, ∞) conjugate indices) if and only if F has the UMDP.
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