Asymptotics of Bergman polynomials for domains with reflection-invariant corners

We study the asymptotic behavior of the Bergman orthogonal polynomials (pₙ)ₙ₌₀∞ for a class of bounded simply connected domains D. The class is defined by the requirement that conformal maps φ of D onto the unit disk extend analytically across the boundary L of D, and that φ' has a finite number of zeros z₁,…, zq on L. The boundary L is then piecewise analytic with corners at the zeros of φ'. A result of Stylianopoulos implies that a Carleman-type strong asymptotic formula for pₙ holds on the exterior domain C̄. We prove that the same formula remains valid across L₁,…,zq\ and on a maximal open subset of D. As a consequence, the only boundary points that attract zeros of pₙ are the corners. This is in stark contrast to the case when φ fails to admit an analytic extension past L, since when this happens the zero counting measure of pₙ is known to approach the equilibrium measure for L along suitable subsequences.