Article ID Journal Published Year Pages File Type
4665285 Advances in Mathematics 2015 21 Pages PDF
Abstract

We extend the result of Lavrentiev which asserts that the harmonic measure and the arc-length measure are A∞A∞ equivalent in a chord-arc Jordan domain. By using this result we extend the classical result of Lindelöf to the class of quasiconformal (q.c.) harmonic mappings by proving the following assertion. Assume that f is a quasiconformal harmonic mapping of the unit disk U onto a Jordan domain. Then the function A(z)=arg⁡(∂φ(f(z))/z)A(z)=arg⁡(∂φ(f(z))/z) where z=reiφz=reiφ, is well-defined and smooth in U⁎={z:0<|z|<1}U⁎={z:0<|z|<1} and has a continuous extension to the boundary of the unit disk if and only if the image domain has C1C1 boundary.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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