Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 626-644 |
| Seitenumfang | 19 |
| Fachzeitschrift | Mathematische Nachrichten |
| Jahrgang | 281 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - 7 Apr. 2008 |
| Extern publiziert | Ja |
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 H(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 H(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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Mathematische Nachrichten, Jahrgang 281, Nr. 5, 07.04.2008, S. 626-644.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Hardy spaces and integral formulas for DFN-domains with arbitrary boundary
AU - Bauer, Wolfram
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/4/7
Y1 - 2008/4/7
N2 - 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 H(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 H(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.
AB - 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 H(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 H(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.
KW - DFN-domains
KW - Hardy and Bergman spaces
KW - Holomorphic liftings
KW - Integral formulas
UR - http://www.scopus.com/inward/record.url?scp=55449137306&partnerID=8YFLogxK
U2 - 10.1002/mana.200610631
DO - 10.1002/mana.200610631
M3 - Article
AN - SCOPUS:55449137306
VL - 281
SP - 626
EP - 644
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 5
ER -