Bergman and Bloch spaces of vector-valued functions

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(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 fac...

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Bibliographic Details
Published in:	Mathematische Nachrichten Vol. 261-262; no. 1; pp. 3 - 22
Main Authors:	Arregui, José Luis, Blasco, Oscar
Format:	Journal Article
Language:	English
Published:	Berlin WILEY-VCH Verlag 01.12.2003 WILEY‐VCH Verlag
Subjects:	Bergman kernels projections in Banach spaces Spaces of vector-valued analytic functions
ISSN:	0025-584X, 1522-2616
Online Access:	Get full text
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Summary:	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(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)
Bibliography:	ArticleID:MANA200310109 istex:58E9703C4804C22B2C7873558049C572DD7183A1 ark:/67375/WNG-70ZD3B87-R Phone: +34 963544729, Fax: +34 963544360
ISSN:	0025-584X 1522-2616
DOI:	10.1002/mana.200310109