Bloch-type spaces and extended Cesàro operators in the unit ball of a complex Banach space

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（4）
• 页码范围: 617-628
• 页数: 12页
• 语种: 英文

摘要

Let B be the unit ball of a complex Banach space X.In this paper,we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative.Next,we define an extended Cesàro operator Tφ with the holomorphic symbol φ and characterize those φ for which Tφ is bounded between the Bloch-type spaces and the little Bloch-type spaces.We also characterize those φ for which Tφ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ.When B is the open unit ball of a finite dimensional complex Banach space X,this additional assumption is automatically satisfied.