Polynomial approximation in the mean with respect to harmonic measure on crescents. II (Q1191894)

[For part I, Trans. Am. Math. Soc. 303, 193-199 (1987; Zbl 0626.30031).] The author studies a problem of density of the polynomials in the Hardy spaces \(H^ s\), \(1\leq s<\infty\), on crescents, i.e. planar domains bounded by two Jordan curves which intersect in a single point such that one of the curves is internal to the other. The paper answers the question for a large class of crescents. Three necessary and sufficient conditions characterizing the density of the polynomials are given in terms of geometric characteristics of the crescent \(E\) near its multiple boundary point, the distribution of its harmonic measure on its ``outer'' boundary \(\partial_ \infty E\) and the density of the polynomials in \(L^ s\) on \(\partial_ \infty E\).