Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 764-785 |
| Seitenumfang | 22 |
| Fachzeitschrift | Mathematische Nachrichten |
| Jahrgang | 281 |
| Ausgabenummer | 6 |
| Publikationsstatus | Veröffentlicht - 5 Mai 2008 |
| Extern publiziert | Ja |
Abstract
Let E be a DFN-space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space H(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ-square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels Kμ on the diagonal and we give an application of our results to liftings of μ-square integrable Banach space valued holomorphic functions over U.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Mathematische Nachrichten, Jahrgang 281, Nr. 6, 05.05.2008, S. 764-785.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Holomorphic liftings and Bergman kernel estimates for DFN-domains
AU - Bauer, Wolfram
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/5/5
Y1 - 2008/5/5
N2 - Let E be a DFN-space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space H(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ-square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels Kμ on the diagonal and we give an application of our results to liftings of μ-square integrable Banach space valued holomorphic functions over U.
AB - Let E be a DFN-space and let U ⊂ E be open. By applying the nuclearity of the Fréchet space H(U) of holomorphic functions on U we show that there are finite measures μ on U leading to Bergman spaces of μ-square integrable holomorphic functions. We give an explicit construction for μ by using infinite dimensional Gaussian measures. Moreover, we prove boundary estimates for the corresponding Bergman kernels Kμ on the diagonal and we give an application of our results to liftings of μ-square integrable Banach space valued holomorphic functions over U.
KW - DFN-domains
KW - Holomorphic lifting
KW - Infinite dimensional holomorphy
KW - Nuclear topology
UR - http://www.scopus.com/inward/record.url?scp=55549140209&partnerID=8YFLogxK
U2 - 10.1002/mana.200610640
DO - 10.1002/mana.200610640
M3 - Article
AN - SCOPUS:55549140209
VL - 281
SP - 764
EP - 785
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 6
ER -