Weighted holomorphic Besov spaces on the polydisk
This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let Un be the unit polydisk in Cn and S be the space of functions of regular variation. Let 1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n) and f∈H(Un). The function f is said to be an element of the holomorphic Besov s...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2011/637083 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850223678642454528 |
|---|---|
| author | Anahit V. Harutyunyan Wolfgang Lusky |
| author_facet | Anahit V. Harutyunyan Wolfgang Lusky |
| author_sort | Anahit V. Harutyunyan |
| collection | DOAJ |
| description | This work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let Un be the unit polydisk in Cn and S be the space of functions of regular variation. Let 1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n) and f∈H(Un). The function f is said to be an element of the holomorphic Besov space Bp(ω) if ‖f‖Bp(ω)p=∫Un|Df(z)|p∏j=1nωj(1-|zj|)/(1-|zj|2)2-pdm2n(z)<+∞, where dm2n(z) is the 2n-dimensional Lebesgue measure on Un and D stands for a special fractional derivative of f defined in the paper. For example, if n=1 then Df is the derivative of the function zf(z). |
| format | Article |
| id | doaj-art-44028e40ccb54f6aada92e0158ddee3e |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-44028e40ccb54f6aada92e0158ddee3e2025-08-20T02:05:51ZengWileyJournal of Function Spaces and Applications0972-68022011-01-019111610.1155/2011/637083Weighted holomorphic Besov spaces on the polydiskAnahit V. Harutyunyan0Wolfgang Lusky1Fac. for Inf. and Appl. Math., University of Yerevan, Alek Manukian 1, Yerevan 25, ArmeniaInst. for Math., University of Paderborn, Warburger Str. 100, D-33098 Paderborn, GermanyThis work is an introduction of weighted Besov spaces of holomorphic functions on the polydisk. Let Un be the unit polydisk in Cn and S be the space of functions of regular variation. Let 1≤p<∞,ω=(ω1,…,ωn),ωj∈S(1≤j≤n) and f∈H(Un). The function f is said to be an element of the holomorphic Besov space Bp(ω) if ‖f‖Bp(ω)p=∫Un|Df(z)|p∏j=1nωj(1-|zj|)/(1-|zj|2)2-pdm2n(z)<+∞, where dm2n(z) is the 2n-dimensional Lebesgue measure on Un and D stands for a special fractional derivative of f defined in the paper. For example, if n=1 then Df is the derivative of the function zf(z).http://dx.doi.org/10.1155/2011/637083 |
| spellingShingle | Anahit V. Harutyunyan Wolfgang Lusky Weighted holomorphic Besov spaces on the polydisk Journal of Function Spaces and Applications |
| title | Weighted holomorphic Besov spaces on the polydisk |
| title_full | Weighted holomorphic Besov spaces on the polydisk |
| title_fullStr | Weighted holomorphic Besov spaces on the polydisk |
| title_full_unstemmed | Weighted holomorphic Besov spaces on the polydisk |
| title_short | Weighted holomorphic Besov spaces on the polydisk |
| title_sort | weighted holomorphic besov spaces on the polydisk |
| url | http://dx.doi.org/10.1155/2011/637083 |
| work_keys_str_mv | AT anahitvharutyunyan weightedholomorphicbesovspacesonthepolydisk AT wolfganglusky weightedholomorphicbesovspacesonthepolydisk |