Details
| Original language | English |
|---|---|
| Pages (from-to) | 764-785 |
| Number of pages | 22 |
| Journal | Mathematische Nachrichten |
| Volume | 281 |
| Issue number | 6 |
| Publication status | Published - 5 May 2008 |
| Externally published | Yes |
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.
Keywords
- DFN-domains, Holomorphic lifting, Infinite dimensional holomorphy, Nuclear topology
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Nachrichten, Vol. 281, No. 6, 05.05.2008, p. 764-785.
Research output: Contribution to journal › Article › Research › 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 -