The Faber Operator and its Boundedness Original Research Article

Let G be a domain bounded by a Jordan curve Γ, and let A(G) be the Banach space of functions continuous on G and holomorphic in G. The Faber operator T is a linear mapping from A(D) to A(G) mapping wn onto the nth Faber polynomial Fn(z) (n=0, 1, 2, …). We show that ‖T‖<∞ if Γ is piecewise Dini-smooth, and give an example of a quasicircle Γ for which ‖T‖=∞.