| Distortion Theorems and Schlicht Radius for $p$-Bloch Functions |
| Received:July 25, 2011 Revised:February 20, 2012 |
| Key Words:
$p$-Bloch functions distortion theorems schlicht radius Julia' lemma.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11001246) and Natural Science Foundation of Zhejiang Province (Nos.D7080080; Y6090694). |
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| Abstract: |
| In this paper, we establish distortion theorems for both normalized $p$-Bloch functions with branch points and normalized locally univalent $p$-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on $| f'(z)|$ and $\Re f'(z)$. As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when $p=1$, our results reduce to that of Liu and Minda. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.01.005 |
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