| Title:
|
New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces (English) |
| Author:
|
Guo, Xin-Cui |
| Author:
|
Zhou, Ze-Hua |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
331-346 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $u$ be a holomorphic function and $\varphi $ a holomorphic self-map of the open unit disk $\mathbb {D}$ in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators $uC_{\varphi }$ from Zygmund type spaces to Bloch type spaces in $\mathbb {D}$ in terms of $u$, $ \varphi $, their derivatives, and $\varphi ^n$, the $n$-th power of $\varphi $. Moreover, we obtain some similar estimates for the essential norms of the operators $uC_{\varphi }$, from which sufficient and necessary conditions of compactness of $uC_{\varphi }$ follows immediately. (English) |
| Keyword:
|
weighted composition operator |
| Keyword:
|
Zygmund type space |
| Keyword:
|
Bloch type space |
| Keyword:
|
essential norm |
| MSC:
|
26A24 |
| MSC:
|
30H30 |
| MSC:
|
47B33 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 06486949 |
| idMR:
|
MR3360429 |
| DOI:
|
10.1007/s10587-015-0178-1 |
| . |
| Date available:
|
2015-06-16T17:39:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144272 |
| . |
| Reference:
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| . |
