Reinhardt Domains with a Cusp at the Origin

Let Ω be a bounded pseudoconvex Reinhardt domain in C with many strictly pseudoconvex points and logarithmic image ω. It was known that the maximal ideal in H∞(Ω) consisting of all functions vanishing at (p1, p2) ∈ Ω is generated by the coordinate functions z1 − p1, z2 − p2 (meaning that one can solve the Gleason problem for H∞(Ω)) if ω is bounded. We show that one can solve Gleason’s problem for H∞(Ω) as well if there are positive numbers a, b and a positive rational number k l such that Ω looks like {(z1, z2) ∈ C : a|z2| ≤ |z1| ≤ b|z2|} for small z.