Order of approximation by electrostatic fields due to electrons (Q1070470)

Let D be a Jordan domain in the complex plane and \(A_ q(D)\) the Bers space with norm \(\|\) \(\|_ q\). If D is the unit disk, it is known that \(\| S_ n\|_ 2\geq \pi /18\), where \(S_ n=\sum^{n}_{k=1}1/(z-z_{nk})\) with \(z_{nk}\in \partial D\), so that approximation in \(\|\) \(\|_ q\), \(q\leq 2\), is not possible. In this paper, we give an order of estimate of \(\| f-S_ n\|_ q\) for \(2<q<\infty\) when \(\partial D\) is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.