| Title:
|
Boundary functions on a bounded balanced domain (English) |
| Author:
|
Kot, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
371-379 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We solve the following Dirichlet problem on the bounded balanced domain $\Omega $ with some additional properties: For $p>0$ and a positive lower semi-continuous function $u$ on $\partial \Omega $ with $u(z)=u(\lambda z)$ for $|\lambda |=1$, $z\in \partial \Omega $ we construct a holomorphic function $f\in \Bbb O(\Omega )$ such that $u(z)=\int _{\Bbb Dz}|f|^pd \frak L_{\Bbb Dz}^2$ for $z\in \partial \Omega $, where $\Bbb D=\{\lambda \in \Bbb C\:|\lambda |<1\}$. (English) |
| Keyword:
|
boundary behavior of holomorphic functions |
| Keyword:
|
exceptional sets |
| Keyword:
|
boundary functions |
| Keyword:
|
Dirichlet problem |
| Keyword:
|
Radon inversion problem |
| MSC:
|
30B30 |
| MSC:
|
30D60 |
| idZBL:
|
Zbl 1224.30005 |
| idMR:
|
MR2532382 |
| . |
| Date available:
|
2010-07-20T15:13:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140486 |
| . |
| Reference:
|
[1] Globevnik, J.: Holomorphic functions which are highly nonintegrable at the boundary.Isr. J. Math. 115 (2000), 195-203. Zbl 0948.32015, MR 1749678, 10.1007/BF02810586 |
| Reference:
|
[2] Jakóbczak, P.: The exceptional sets for functions from the Bergman space.Port. Math. 50 (1993), 115-128. MR 1300590 |
| Reference:
|
[3] Jakóbczak, P.: Highly non-integrable functions in the unit ball.Isr. J. Math. 97 (1997), 175-181. MR 1441246, 10.1007/BF02774034 |
| Reference:
|
[4] Jakóbczak, P.: 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:
|
[5] Kot, P.: Description of simple exceptional sets in the unit ball.Czech. Math. J. 54 (2004), 55-63. Zbl 1052.30006, MR 2040218, 10.1023/B:CMAJ.0000027246.96443.28 |
| Reference:
|
[6] Kot, P.: Boundary functions in $L^2H(\Bbb B^n)$.Czech. Math. J. 57 (2007), 29-47. MR 2309946, 10.1007/s10587-007-0041-0 |
| Reference:
|
[7] Kot, P.: Homogeneous polynomials on strictly convex domains.Proc. Am. Math. Soc. 135 (2007), 3895-3903. Zbl 1127.32005, MR 2341939, 10.1090/S0002-9939-07-08939-3 |
| Reference:
|
[8] Kot, P.: Bounded holomorphic functions with given maximum modulus on all circles.Proc. Amer. Math. Soc 137 (2009), 179-187. Zbl 1157.32001, MR 2439439, 10.1090/S0002-9939-08-09468-9 |
| . |
