Multipliers between $ BMO $ Spaces on Open Unit Ball
Multipliers between $ BMO $ Spaces on Open Unit Ball
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DOI：
10.1007/s000200300003
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发表时间：
2003-02
影响因子：
0.8
通讯作者：
James Li-Ming Wang;Zhijian Wu
中科院分区：
文献类型：
--
作者：
James Li-Ming Wang;Zhijian Wu
$ BMO $和$ VMO $空间由开单位球上的所有局部可积函数组成，使得它们在任何Bergman球上的平均振荡分别是有界的，并且当Bergman球接近单位球的边界时消失为零。$ BMO $和$ VMO $空间的调和（或解析）版本分别是Bloch空间和小Bloch空间。这些空间的研究在现代分析中起着重要的作用，特别是在算子理论和全纯空间领域。本文系统地刻画了$ BMO $和$ VMO $空间的乘子.
$ BMO $ and $ VMO $ spaces consist of all those locally integrable functions on the open unit ball such that their mean oscillations on any Bergman ball are, respectively, bounded and vanishing to zero as the Bergman ball approaches the boundary of the unit ball. The harmonic (or analytic) versions of the $ BMO $ and $ VMO $ spaces are the Bloch space and the little Bloch space, respectively. The study of these spaces plays an important role in modern analysis, especially in the the area of operator theory and holomorphic spaces. In this paper, we characterize systematically the multipliers of $ BMO $and $ VMO $ spaces.