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Volume 34, Issue 3
Some Characterizations of Bloch Functions

Guanghua He

Anal. Theory Appl., 34 (2018), pp. 225-231.

Published online: 2018-11

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  • Abstract

We define Bloch-type functions of $\mathcal{C}^1(\mathbb{D})$ on the unit disk of complex plane $\mathbb{C}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_{\phi}$ acting between two Bloch-type spaces. These obtained results generalize the corresponding known ones to the setting of $\mathcal{C}^1(\mathbb{D})$.

  • AMS Subject Headings

11K70, 32A70

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COPYRIGHT: © Global Science Press

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@Article{ATA-34-225, author = {Guanghua He}, title = {Some Characterizations of Bloch Functions}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {3}, pages = {225--231}, abstract = {

We define Bloch-type functions of $\mathcal{C}^1(\mathbb{D})$ on the unit disk of complex plane $\mathbb{C}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_{\phi}$ acting between two Bloch-type spaces. These obtained results generalize the corresponding known ones to the setting of $\mathcal{C}^1(\mathbb{D})$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0059}, url = {http://global-sci.org/intro/article_detail/ata/12837.html} }
TY - JOUR T1 - Some Characterizations of Bloch Functions AU - Guanghua He JO - Analysis in Theory and Applications VL - 3 SP - 225 EP - 231 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2017-0059 UR - https://global-sci.org/intro/article_detail/ata/12837.html KW - Bloch space, majorant, composition operator. AB -

We define Bloch-type functions of $\mathcal{C}^1(\mathbb{D})$ on the unit disk of complex plane $\mathbb{C}$ and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator $C_{\phi}$ acting between two Bloch-type spaces. These obtained results generalize the corresponding known ones to the setting of $\mathcal{C}^1(\mathbb{D})$.

Guanghua He. (2018). Some Characterizations of Bloch Functions. Analysis in Theory and Applications. 34 (3). 225-231. doi:10.4208/ata.OA-2017-0059
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