On the growth of minimal positive harmonic functions in a plane region
Let D be a planar domain bounded by an infinite number of analytic Jordan curves {C/} whose only one clustering point is the point at infinity. Let P(D) be the class of positive harmonic functions in D with the vanishing boundary value at any finite boundary point. Let G(D) and K(D) be two subclasses of P(D) such that u e G(D) is equivalent to Γ 0 0< I -^—u(z)ds<oo J ΣI Cv on and u e K(D) is equivalent to