Estimates on \(\mu(z)\)-homeomorphisms of the unit disk (Q5935816)
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scientific article; zbMATH DE number 1611099
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimates on \(\mu(z)\)-homeomorphisms of the unit disk |
scientific article; zbMATH DE number 1611099 |
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Estimates on \(\mu(z)\)-homeomorphisms of the unit disk (English)
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20 November 2002
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Let \(f\) be a \(K\)-quasiconformal mapping of the unit disk \(\Delta\) onto itself with the normalization \(f(0)= 0\) then holds Mori's result \[ |f(z_1)- f(z_2)|\leq 16|z_1- z_2|^{1/K},\quad z_1,z_2\in\Delta. \] The aim of this paper is to generalize this to \(\mu(z)\)-homeomorphisms of \(\Delta\) (for \(\mu(z)\)-homeomorphisms see \textit{M. A. Brakalova} and \textit{J. A. Jenkins} [J. Anal. Math. 76, 67-92 (1998; Zbl 0921.30015)]).
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\(\mu(z)\)-homeomorphisms
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\(K\)-quasiconformal mapping
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