多复变中Bloch空间到BMOA空间的拉回

Bloch-to-BMOA Pullbacks in Several Complex Variables

设φ是从单位球B^m到单位多圆柱D^n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H^2(B^m)代替。BMOA空间,类似结论仍然成立.

For a given holomorphic map φ from unit ball Bm 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 Bn on Dn to BMOA on BM holds. The same result holds when BMOA space is taken by H2（Bm）.