Hausdorff-summability of power series i

Let A be a regular summability method and P(w)=a_kw^k a power series with positive radius of convergence. A theorem of Okada states, that P(w) is summable (A) for w in the region, where M_P is the Mittag-Leffler-star of P and R_A is the largest star-shaped open region, such that w^k is uniformly summable (A) on each of its compact subsets. The question remains open, whether P(w) might be summable (A) when w is outside of the closure of G. In this paper the question is answered for the class of Hausdorff methods.