On harmonic Bloch-type mappings
Let $f$ be a complex-valued harmonic mapping defined in the unit disk $\mathbb D$. We introduce the following notion: we say that $f$ is a Bloch-type function if its Jacobian satisfies $$ \sup_{z\in\mathbb D}(1-|z|^2)\sqrt{|J_f(z)|}0$ and a univalent $\psi$ such that $\varphi = c \log \psi'$.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | Let $f$ be a complex-valued harmonic mapping defined in the unit disk
$\mathbb D$. We introduce the following notion: we say that $f$ is a Bloch-type
function if its Jacobian satisfies $$ \sup_{z\in\mathbb
D}(1-|z|^2)\sqrt{|J_f(z)|}0$ and a
univalent $\psi$ such that $\varphi = c \log \psi'$. |
|---|---|
| DOI: | 10.48550/arxiv.1607.04626 |