Details
| Original language | English |
|---|---|
| Pages (from-to) | 626-644 |
| Number of pages | 19 |
| Journal | Mathematische Nachrichten |
| Volume | 281 |
| Issue number | 5 |
| Publication status | Published - 7 Apr 2008 |
| Externally published | Yes |
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.
Keywords
- DFN-domains, Hardy and Bergman spaces, Holomorphic liftings, Integral formulas
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Nachrichten, Vol. 281, No. 5, 07.04.2008, p. 626-644.
Research output: Contribution to journal › Article › Research › 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 -