We provide a counterexample (a strongly convex domain in C 3 C^3 ) to a statement about certain extremal bases in the papers of J. D. McNeal in 1992 and 1994 which was used to prove estimates for the Bergman kernel and invariant metrics. We also prove that those estimates in fact remain correct for the same bases (other authors had introduced different bases to fix this).
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Николов et al. (2013) studied this question.