| P-Bloch函数的偏差定理和单叶半径 |
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| 引用本文： | 郑小慧,王建飞. P-Bloch函数的偏差定理和单叶半径[J]. 数学研究及应用, 2013, 33(1): 45-53 |
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| 作者姓名： | 郑小慧 王建飞 |
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| 作者单位： | 浙江师范大学数理信息学院, 浙江 金华 321004;浙江师范大学数理信息学院, 浙江 金华 321004 |
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| 基金项目： | 国家自然科学基金(Grant No.11001246); 浙江省自然科学基金(Grant Nos.D7080080;Y6090694). |
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| 摘 要： | 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 ■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.
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| 关 键 词： | p-Bloch functions distortion theorems schlicht radius Julia’lemma. |
| 收稿时间： | 2011-07-25 |
| 修稿时间： | 2012-02-20 |
Distortion Theorems and Schlicht Radius for $p$-Bloch Functions |
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| Xiaohui ZHENG and Jianfei WANG. Distortion Theorems and Schlicht Radius for $p$-Bloch Functions[J]. Journal of Mathematical Research with Applications, 2013, 33(1): 45-53 |
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| Authors: | Xiaohui ZHENG and Jianfei WANG |
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| Affiliation: | Department of Mathematics and Physics, Information Engineering, Zhejiang Normal University, Zhejiang 321004, P. R. China;Department of Mathematics and Physics, Information Engineering, Zhejiang Normal University, Zhejiang 321004, P. R. China |
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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. |
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| Keywords: | $p$-Bloch functions distortion theorems schlicht radius Julia' lemma. |
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