  Let \Omega\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We
show that a harmonic function in \Omega that is Lipschitz along a family of
curves transversal to b\Omega is Lipschitz in \Omega. The space of Lipschitz
functions we consider is defined using the notion of a majorant which is a
certain generalization of the power functions t^\alpha, 0<\alpha<1.
