| Title:
|
Some characterizations of harmonic Bloch and Besov spaces (English) |
| Author:
|
Fu, Xi |
| Author:
|
Lu, Bowen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
417-430 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega $-$\alpha $-Bloch space and characterize it in terms of $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{x-y}\Big | $$ and $$ \omega ((1-|x|^2)^\beta (1-|y|^2)^{\alpha - \beta }) \Big | \frac {f(x)-f(y)}{|x|y-x'}\Big | $$ where $\omega $ is a majorant. Similar results are extended to harmonic little $\omega $-$\alpha $-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kähler (2005). (English) |
| Keyword:
|
harmonic function |
| Keyword:
|
Bloch space |
| Keyword:
|
Besov space |
| Keyword:
|
majorant |
| MSC:
|
30C20 |
| MSC:
|
31B05 |
| MSC:
|
32A18 |
| idZBL:
|
Zbl 06604476 |
| idMR:
|
MR3519611 |
| DOI:
|
10.1007/s10587-016-0265-y |
| . |
| Date available:
|
2016-06-16T12:50:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145733 |
| . |
| 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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