ESTIMATE OF THE CAUCHY INTEGRAL OVER AHLFORS REGULAR CURVES

Abstract. We obtain the complete characterization of those domains G ⊂ C which admit the so called estimate of the Cauchy integral, that is to say,˛̨̨R ∂G f(z) dz ˛̨̨ ≤ C(G) ‖f‖ ∞ γ(E) for all E ⊂ G and f ∈ H∞(G \ E), where γ(E) is the analytic capacity of E. The corresponding result for continuous functions f and the continuous analytic capacity α(E) is also proved. 1