多复变中Bloch空间到BMOA空间的拉回

数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 851-860.

多复变中Bloch空间到BMOA空间的拉回

方中山^1,2|周泽华¹

1.天津大学数学系天津 300072|2.天津工业大学理学院数学系天津 300387

收稿日期:2010-09-18 修回日期:2012-02-25 出版日期:2012-10-25 发布日期:2012-10-25
基金资助:
国家自然科学基金(10971153, 10671141)资助

Bloch-to-BMOA Pullbacks in Several Complex Variables

FANG Zhong-Shan^1,2, ZHOU Ze-Hua¹

1.Department of Mathematics, Tianjin University, Tianjin 300072|2.Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387

Received:2010-09-18 Revised:2012-02-25 Online:2012-10-25 Published:2012-10-25
Supported by:
国家自然科学基金(10971153, 10671141)资助

摘要/Abstract

摘要：

设φ是从单位球B^m 到单位多圆柱Dⁿ的解析映射, 该文研究了由φ诱导的复合算子从Bloch空间到BMOA空间的拉回性质, 并给出了具有此性质的充要条件. 如果用Hardy空间H²(B^m)代替BMOA空间, 类似结论仍然成立.

关键词: Bloch空间, BMOA空间, 复合算子, 拉回, 多圆柱, 单位球

Abstract:

For a given holomorphic map φ from unit ball B^m to polydisk Dⁿ, the present paper investigates the Bloch-to-BMOA composition property (pullback property) of φ. More precisely, a sufficient and necessary condition is given that the pullback property from the Bloch space B^m on Dⁿ to BMOA on B^m holds. The same result holds when BMOA space is taken by H²(B^m).

Key words: Bloch space, BMOA space, Composition operators, Pullbacks, Polydisc, Unit ball

中图分类号:

47B38

方中山, 周泽华. 多复变中Bloch空间到BMOA空间的拉回[J]. 数学物理学报, 2012, 32(5): 851-860.

FANG Zhong-Shan, ZHOU Ze-Hua. Bloch-to-BMOA Pullbacks in Several Complex Variables[J]. Acta mathematica scientia,Series A, 2012, 32(5): 851-860.

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