Density of the polynomials in Bergman spaces

Abstract

Let G be a bounded simply connected domain in the complex plane. Using a result of Hedberg, we show that the polynomials are dense in Bergman space L^(G) if G is the image of the unit disk U under a weak-star generator of H. We also show that density of the polynomials in L 2 a (G) implies density of the polynomials in H 2 {G).