Journal of the
Korean Mathematical Society JKMS

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball $B$ in $\Bbb C^{n}$. For an M-harmonic function $h$ which satisfies certain integrabilty conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that $h$ is Lipschitz smooth on $B\setminus\Omega$.

Keywords: Bergman metric, Invariant Lipschitz class, M-harmonic function

MSC numbers: Primary 31B25; Secondary; 32A40