Bessel capacity, Hausdorff content and the tangential boundary behavior of harmonic functions (Q674608)

The main result gives some comparison of the Bessel capacity and the Hausdorff content. It is shown that the Bessel capacity of \[ \tilde{E}_{\gamma, c}= \bigcap_{x\in E}B(x,c\delta _E(x)^{\gamma}) \] for \(E \subset \mathbb{R}^n\) can be estimated by the Hausdorff content of \(E\). This is applied to the investigation of the tangential boundary behaviour of harmonic functions in the upper half plane. The results generalize and improve the previous paper [\textit{H. Aikawa} and \textit{A. A. Borichev}, Trans. Am. Math. Soc. 348, 1013-1030 (1996; Zbl 0856.31004)].