Removable sets for harmonic functions
The author shows that a compact subset \(K\subset\mathbb{R}^ d\), \(d\geq 2\), is removable for a harmonic function in the Zygmund class if and only if \(m_{d-1}(K)=0\); here \(m_{d-1}\) dennotes \((d-1)\)-dimensional Hausdorff measure. The author's results imply a simpler proof of Carleson's theorem for removable sets in the class \(\text{Lip} \alpha\), \(0<\alpha<1\), [see \textit{L. Carleson}, Selected problems on exceptional sets (1967; Zbl 0189.109)].
scientific article; zbMATH DE number 59887