Approximation in the mean by bounded analytic functions

Let 1 < p < infinity and 1/p + 1/q = 1. Let C-q denote the Bessel capacity in the plane. Let M(lambda) be the set of homomorphisms phi of H-infinity(G) such that phi(z) = lambda and let NP denote the set of points lambda in partial derivative G for which M(lambda) is not a peak set for H-infinity(G). In this note, we show that if C-q(NP) = 0, then H-infinity(G) is dense in L(a)(p)(G), the Bergman space over G.