Cauchy independent measures and super-additivity of analytic capacity

Alexander Reznikov, Alexander Volberg

Published 2012-11-12Version 1

We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition is essential or not. We apply this result to study the independence of Cauchy integral operators.