Journal of the
Korean Mathematical Society JKMS

In this paper, weighted Bloch spaces $\Cal B_q \quad (q>0)$ are considered on the open unit ball in $\Bbb C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic funcitons. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $\Cal B_q $. It is also proved that weighted Bloch space is a Banach space for each weight $ q>0 $, and the little Bloch space $\Cal B_{q, 0}$ associated with $\Cal B_q $ is a separable subspace of $\Cal B_q $ which is the closure of the polynomials for each $q \geq 1 $.

Keywords: Bergman metric, weighted Bloch spaces, little Bloch space

MSC numbers: 32H25, 32E25, 30C40