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RESEARCH PRODUCT

Bergman and Bloch spaces of vector-valued functions

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We investigate Bergman and Bloch spaces of analytic vector-valued functions in the unit disc. We show how the Bergman projection from the Bochner-Lebesgue space Lp(, X) onto the Bergman space Bp(X) extends boundedly to the space of vector-valued measures of bounded p-variation Vp(X), using this fact to prove that the dual of Bp(X) is Bp(X*) for any complex Banach space X and 1 < p < ∞. As for p = 1 the dual is the Bloch space ℬ(X*). Furthermore we relate these spaces (via the Bergman kernel) with the classes of p-summing and positive p-summing operators, and we show in the same framework that Bp(X) is always complemented in p(X). (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)