Reinhardt domains with a cusp at the origin

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Let V be a bounded pseudoconvex Reinhardt domain in C² with many strictly pseudoconvex points and logarithmic image W. It was known that the maximal ideal in H∞(V) consisting of all functions vanishing at (p,q) in V is generated by the coordinate functions z-p, w-q (meaning that one can solve the Gleason problem for H∞(V)) if W is bounded. We show that one can solve Gleason's problem for H∞(V) as well if there are positive numbers a, b and a positive rational number k/l such that V looks like (z,w) in C²: a |w|ˡ <= |z|ᵏ = b |w|ˡ for small (z,w).