On the Asymptotic Behavior of p-Faber Polynomials for Domains with Piecewise Analytic Boundary

Let G⊂ℂ be a domain bounded by a piecewise analytic Jordan's curve L, and let Fn,p denote the p-Faber polynomials associated with G. We derive estimates of the form Fn,p(z)=O(1/nη), (n→∞) for z∈G, where η depends on geometric properties of L and the parameter p. Also, we show that O cannot be replaced by o in the relation given above.