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Hardy spaces and integral formulas for ℱ-domains with arbitrary boundary

✍ Scribed by Wolfram Bauer

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
261 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let E be the dual of a Fréchet nuclear space, then it is well‐known that for each open set U in E the space ℋ︁(U) of all holomorphic functions on U is a nuclear Fréchet space. Let 𝒜 be a commutative unital Banach sub‐algebra of all bounded holomorphic functions on U which separates points. Applying the nuclearity of ℋ︁(U) we show that the evaluation on U is given by an integral formula over the Shilov boundary of 𝒜. We obtain Szegö‐ and Bergman kernels together with some boundary estimates. Moreover, we show that there is a notion of Hardy and Bergman space for 𝒟ℱ𝒩‐domains with arbitrary boundary. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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