- WEIGHTED BLOCH SPACES IN
- Kyong Taik Hahn ; Ki Seong Choi ;
- Journal of the Korean Mathematical Society, volume 35, issue 1, 1998, Pages 177~189
Abstract
In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. 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 $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.