Bergman and Bloch spaces of vector‐valued functions
Copyright policy )Bergman and Bloch spaces of vector‐valued functions
AbstractWe 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(𝔻, 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 ℬ︁(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 𝓁p(X). (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
- University of La Rioja Spain
- University of Zaragoza Spain
- University of Valencia Spain
Spaces of vector- and operator-valued functions, Banach spaces of continuous, differentiable or analytic functions, Spaces of vector-valued analytic functions, Bergman kernels, spaces of vector-valued analytic functions, projections in Banach spaces, Projections in Banach spaces
Spaces of vector- and operator-valued functions, Banach spaces of continuous, differentiable or analytic functions, Spaces of vector-valued analytic functions, Bergman kernels, spaces of vector-valued analytic functions, projections in Banach spaces, Projections in Banach spaces
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