| Title:
|
$\omega $--weighted holomorphic Besov spaces on the unit ball in $C^n$ (English) |
| Author:
|
Harutyunyan, A. V. |
| Author:
|
Lusky, W. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
37-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The $\omega$-weighted Besov spaces of holomorphic functions on the unit ball $B^n$ in $C^n$ are introduced as follows. Given a function $\omega $ of regular variation and $0< p< \infty $, a function $f$ holomorphic in $B^n$ is said to belong to the Besov space $B_p(\omega)$ if $$ \Vert f\Vert^p_{B_p(\omega )}=\int_{B^n} (1-|z|^2)^p|Df(z)|^p \frac{\omega(1-|z|)}{(1-|z|^2)^{n+1}}\,d\nu(z)< +\infty , $$ where $d\nu (z)$ is the volume measure on $B^n$ and $D$ stands for the fractional derivative of $f$. The holomorphic Besov space is described in the terms of the corresponding $L_p(\omega )$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also, explicit descriptions of the duals of the considered Besov spaces are given. (English) |
| Keyword:
|
weighted Besov spaces |
| Keyword:
|
unit ball |
| Keyword:
|
projection |
| MSC:
|
32C37 |
| MSC:
|
46E15 |
| MSC:
|
46T25 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 1240.32017 |
| idMR:
|
MR2828371 |
| . |
| Date available:
|
2011-03-08T17:35:57Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141427 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
