Width of the Gakhov class over the Dirichlet space is equal to 2

Аннотация

Gakhov class G is formed by the holomorphic and locally univalent functions in the unit disk with no more than unique critical point of the conformal radius. Let D be the classical Dirichlet space, and let P: f ↦ F = f″/f′. We prove that the radius of the maximal ball in P(G)∩D with the center at F = 0 is equal to 2.