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

Abstract

We compare the Bessel capacity with the Hausdorff content. For E ⊂ Rn we let e Eγ,c = S x∈E B(x, cδE(x) γ) with c > 0 and 0 < γ ≤ 1. If E is an open set and 0 < γ < 1, then e Eγ,c is larger than E. It is shown that the Bessel capacity of e Eγ,c is estimated above by the Hausdorff content of E. This estimation is applied to the tangential boundary behavior of harmonic functions in the upper half space.