Journal of the
Korean Mathematical Society JKMS

Let $B$ be the open unit ball with center $0$ in the complex space ${\mathbb C}^n.$ For each $q>0$, $\mathcal B_q $ consists of holomorphic functions $f:B \rightarrow \mathbb C $ which satisfy $$ \sup_{z \in B} (1 - \parallel z \parallel^2)^q \parallel {\bigtriangledown} f(z) \parallel \ < \ \infty \ . $$ In this paper, we will show that functions in weighted Bloch spaces $\mathcal B_q$ $(0 < q < 1)$ satifies the following Lipschitz type result for Bergman metric $\beta$: $$ \vert f(z) - f(w) \vert < C \beta(z, w) $$ for some constant $C$.

Keywords: Bergman metric, weighted Bloch spaces, Besov space, BMO

MSC numbers: 32H25, 32E25, 30C40