| Title:
|
Boundary functions in $L^2H(\mathbb{B}^n)$ (English) |
| Author:
|
Kot, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
29-47 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function $u$ which is lower semi-continuous on $\partial \mathbb{B}^{n}$ we give necessary and sufficient conditions in order that there exists a holomorphic function $f\in \mathbb{O}(\mathbb{B}^{n})$ such that \[ u(z)=\int _{|\lambda |<1}\left|f(\lambda z)\right|^{2}\mathrm{d}{\mathfrak L}^{2}(\lambda ). \] (English) |
| Keyword:
|
boundary behavior of holomorphic functions |
| Keyword:
|
exceptional sets |
| Keyword:
|
boundary functions |
| Keyword:
|
computed tomography |
| Keyword:
|
Dirichlet problem |
| MSC:
|
30B30 |
| MSC:
|
32A10 |
| MSC:
|
32A40 |
| idZBL:
|
Zbl 1174.30001 |
| idMR:
|
MR2309946 |
| . |
| Date available:
|
2009-09-24T11:43:31Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128152 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] J. Globevnik: Holomorphic functions which are highly nonintegrable at the boundary.Isr. J. Math. 115 (2000), 195–203. Zbl 0948.32015, MR 1749678 |
| Reference:
|
[4] P. Jakóbczak: The exceptional sets for functions from the Bergman space.Port. Math. 50 (1993), 115–128. MR 1300590 |
| Reference:
|
[5] P. Jakóbczak: The exceptional sets for holomorphic functions in Hartogs domains, Complex Variables.Theory Appl. 32 (1997), 89–97. MR 1448482, 10.1080/17476939708814981 |
| Reference:
|
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| Reference:
|
[7] P. Jakóbczak: Highly non-integrable functions in the unit ball.Isr. J. Math. 97 (1997), 175–181. 10.1007/BF02774034 |
| Reference:
|
[8] P. Jakóbczak: Exceptional sets of slices for functions from the Bergman space in the ball.Can. Math. Bull. 44 (2001), 150–159. MR 1827853, 10.4153/CMB-2001-019-7 |
| Reference:
|
[9] P. Kot: Description of simple exceptional sets in the unit ball.Czechoslovak Math. J. 54 (2004), 55–63. Zbl 1052.30006, MR 2040218, 10.1023/B:CMAJ.0000027246.96443.28 |
| Reference:
|
[10] P. Pflug: oral communication, 4-th Symposium on Classical Analysis, Kazimierz.(1987). |
| Reference:
|
[11] W. Rudin: Function theory in the unit ball of $\mathbb{C}^{n}$.Springer, New York, 1980. MR 0601594 |
| Reference:
|
[12] P. Wojtaszczyk: On highly nonintegrable functions and homogeneous polynomials.Ann. Pol. Math. 65 (1997), 245–251. Zbl 0872.32001, MR 1441179, 10.4064/ap-65-3-245-251 |
| . |
