Boundary Estimates for Bergman Polynomials in Domains with Corners

Let G be a bounded simply-connected domain in the complex plane C, whose boundary Γ := ∂G is a Jordan curve, and let {pn}n=0 denote the sequence of Bergman polynomials of G. This is defined as the unique sequence of polynomials {pn(z)}n=0, with positive leading coefficient, that are orthonormal with respect to the area measure on G. The asymptotic behaviour of pn(z) in the exterior of Γ, in cases when Γ is a piecewise analytic Jordan curve have been established recently in [15]. The purpose of this note is to derive, for the same class of curves, estimates for the asymptotics of pn(z) on Γ. Dedication: To Ed Saff, an outstanding mathematician, a great mentor and collaborator, and a dear friend, on the occasion of his 70th birthday.