A universal criterion for quasi-analytic classes in Jordan domains

Carleman classes in Jordan domains in the complex plane are investigated. A criterion for regular Carleman classes to be quasi-analytic is established, which is universal in a certain sense for all weakly uniform domains. The proof is based on a solution of the Dirichlet problem with unbounded boundary function, and a result on bounds for the harmonic measure due to Beurling plays a substantial role. Bibliography: 20 titles.