Area criteria for functions to be Bloch, normal, and Yosida (Q796686)
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scientific article; zbMATH DE number 3865666
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Area criteria for functions to be Bloch, normal, and Yosida |
scientific article; zbMATH DE number 3865666 |
Statements
Area criteria for functions to be Bloch, normal, and Yosida (English)
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1983
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Let f be meromorphic in the unit disc. The author shows that f is normal if and only if there exist \(r>0\) and \(\alpha<\pi\) such that the spherical area of the image of every non-Euclidean disc \(\{| z-z_ 0| /| 1-\bar z_ 0z|<r\}\) is bounded by \(\alpha\). A related result is proved for functions in the plane.
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Yoshida
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Bloch function
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normal
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spherical area
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