Removable sets of functions of classes of BMO and their generalizations (Q1102483)

Some theorems are proved concerning removable singularities for harmonic or analytic functions of the class BMO. We reproduce one of them (Theorem 2). Suppose D is a domain in \({\mathbb{R}}^ n\) (n\(\geq 3)\). A compact set \(K\subset D\) is a removable singularity for all functions \(f\in BMO(D)\) which are harmonic in \(D\setminus K\) if and only if \(mes_{n-2}K=0\). For analytic functions in BMO(D) \((D\subset {\mathbb{C}}^ n\), \(n\geq 1)\) only sufficient conditions are given \((mes_{n-2}K=0\) has to be replaced by \(mes_{2n-1}K=0\) in correspondence with general results [see \textit{R. Harvey} and \textit{J. C. Polking}, Acta Math. 125, 39-56 (1970; Zbl 0214.100)].