arXiv subjects
Publications and source records attributed to V. Liontou.
We show that if an open arc J of the boundary of a Jordan domain $Ω$ is rectifiable, then the derivative $Φ$' of the Riemann map $Φ: D\rightarrow Ω$ from the open unit disk D onto $Ω$ behaves as an $H^1$ function when we approach the arc $Φ^{-1}(J^{\prime})$,where $J^{\prime}$ is any compact subarc of $J$. "
If a Jordan curve σ has a one-sided conformal collar with "good" properties, then, using the Reflection principle, we show that any other conformal collar of σ from the same side has the same "good" properties. A particular use of this fact concerns analytic Jordan curves, but in general the Jordan arcs we consider do not have to be analytic. We show that if an one-sided conformal collar bounded by σ is of class A^p, then any other collar bounded by σ and from the same side of σ is of class A^p.