**G. Khuskivadze, V. Paatashvili**

## On a Representation of the Derivative of a Conformal Mapping

**abstract:**

Let $\om$ 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 $\lg\om'$ to be represented
in the unit circle by a Cauchy type $A$-integral with density $\arg\om'$,
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 $\lg\om'$ belong to the Hardy class $H_1$