Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEIGHTED BLOCH SPACES IN $C^n$

  • Kyong Taik Hahn (Department of Mathematics The Pennsylvania State University University Park, PA 16802 USA and Department of Mathematics Konyang university NonSan 320-800, Korea) ;
  • Ki Seong Choi (Department of Mathematics Konyang of university NonSan 320-800, Korea)
  • Published : 1998.02.01
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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 $q \geq 1$.

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References

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