On a Representation of the Derivative of a Conformal Mapping
Givi Khuskivadze, Vakhtang Paatashvili · Georgian Mathematical Journal · 2001
Let ω conformally map the unit circle on a plane singly-connected domain D bounded by a simple rectifiable curve. It is shown that for the function lg ω ′ to be represented in the unit circle by a Cauchy type A -integral with density arg ω ′, it is necessary and sufficient that D be a Smirnov domain. In particular, for this representation to be done by a Cauchy–Lebesgue type integral with the same density, it is necessary and sufficient that the function lg ω ′ belong to the Hardy class H 1 .