ABSTRACT
To deduce the transformation laws for the Szego˝ projection and kernel under conformal mappings, we will require the following result.
Theorem 12.1. Suppose that f : Ω1 → Ω2 is a biholomorphic mapping between bounded domains with C∞ smooth boundaries. Then f ∈ C∞(Ω1) and f
′ is nonvanishing on Ω1. Consequently, f −1 ∈ C∞(Ω2).
Furthermore, f ′ is equal to the square of a function in A∞(Ω1).
