New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo; Ze-Hua Zhou

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 331-346
  • ISSN: 0011-4642

Abstract

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Let u be a holomorphic function and ϕ a holomorphic self-map of the open unit disk 𝔻 in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators u C ϕ from Zygmund type spaces to Bloch type spaces in 𝔻 in terms of u , ϕ , their derivatives, and ϕ n , the n -th power of ϕ . Moreover, we obtain some similar estimates for the essential norms of the operators u C ϕ , from which sufficient and necessary conditions of compactness of u C ϕ follows immediately.

How to cite

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Guo, Xin-Cui, and Zhou, Ze-Hua. "New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces." Czechoslovak Mathematical Journal 65.2 (2015): 331-346. <http://eudml.org/doc/270082>.

@article{Guo2015,
abstract = {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.},
author = {Guo, Xin-Cui, Zhou, Ze-Hua},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted composition operator; Zygmund type space; Bloch type space; essential norm},
language = {eng},
number = {2},
pages = {331-346},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces},
url = {http://eudml.org/doc/270082},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Guo, Xin-Cui
AU - Zhou, Ze-Hua
TI - New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 331
EP - 346
AB - 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.
LA - eng
KW - weighted composition operator; Zygmund type space; Bloch type space; essential norm
UR - http://eudml.org/doc/270082
ER -

References

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