Density of rational functions in hardy Bergman spaces

Let G be a bounded finitely connected domain in the complex plane such that no component of partial derivative G reduces to a point. Let A(G) be the set of all functions analytic on G and continuous on (G) over bar and let R((G) over bar) be the closure of all rational functions with poles off (G) over bar. In this paper, we investigate the problem of when A(G) (R((G) over bar)) is dense in the Hardy space H-q (G). We give several equivalent conditions under which A(G) is dense in H-q(G). We also show that if G is simply connected, then A(G) is dense in H-2 (G) if and only if A(G) is dense in L-a(2).(G).