Bounded $\lambda$-harmonic functions in domains of ${\mathbb{H}}^n$ with asymptotic boundary with fractional dimension

Leonardo Prange Bonorino, Patrícia Kruse Klaser

The existence and nonexistence of $\lambda$-harmonic functions in unbounded domains of ${\mathbb{H}}^n$ are investigated. We prove that if the $(n-1)/2$ Hausdorff measure of the asymptotic…