One sided conformal collars and the reflection principle

Abstract

If a Jordan curve {\sigma} has a one-sided conformal collar with "good" properties, then, using the Reflection principle, we show that any other conformal collar of {\sigma} 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 {\sigma} is of class A^p, then any other collar bounded by {\sigma} and from the same side of {\sigma} is of class A^p.