Approximation in the mean by polynomials (Q5903076)

The author gives a condition on crescent shaped regions \(\Omega\) which insures that the polynomials are dense in the Bergman spaces \(A^ p(\Omega)\). This condition is compared to some classical results. Moreover, a characterization of the dual of \(A^ p(\Omega)\) \((1<p<\infty)\) is given for regions bounded by two internally tangent circles. The latter is achieved by using a theorem on the boundedness of the Bergman projection on \(L^ p(\Omega)\) [see also the reviewer, Ark. Mat. 18, 207-221 (1980; Zbl 0484.30009)].