Bessel capacity, Hausdorff content and the tangential boundary behavior of harmonic functions
Hiroaki Aikawa · Hiroshima Mathematical Journal · 1996
Abstract. We compare the Bessel capacity with the Hausdorff content. For E ⊂ Rn we let eEγ,c = Sx∈E B(x, cδE(x)γ) with c> 0 and 0 < γ ≤ 1. If E is an open set and 0 < γ < 1, then eEγ,c is larger than E. It is shown that the Bessel capacity of eEγ,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. 1.