The planar Cantor sets of zero analytic capacity and the local 𝑇(𝑏)-Theorem

Abstract

In this paper we obtain rather precise estimates for the analytic capacity of a big class of planar Cantors sets. In fact, we show that analytic capacity and positive analytic capacity are comparable for these sets. The main tool for the proof is an appropriate version of the T ( b ) T(b) -Theorem.