龙见仁, 伍鹏程. 从加权Bloch空间到Qk(p,q)空间的复合算子[J]. 华南师范大学学报(自然科学版), 2012, 44(1).
引用本文: 龙见仁, 伍鹏程. 从加权Bloch空间到Qk(p,q)空间的复合算子[J]. 华南师范大学学报(自然科学版), 2012, 44(1).
Composition operators from weighted Bloch spaces to Qk(p,q) spaces[J]. Journal of South China Normal University (Natural Science Edition), 2012, 44(1).
Citation: Composition operators from weighted Bloch spaces to Qk(p,q) spaces[J]. Journal of South China Normal University (Natural Science Edition), 2012, 44(1).

从加权Bloch空间到Qk(p,q)空间的复合算子

Composition operators from weighted Bloch spaces to Qk(p,q) spaces

  • 摘要: 假设\phi是单位圆D上一个解析自映射,X是单位圆D上一个Banach空间. 定义X上复合算子:C_\phi: C_\phi(f)=f o \phi,对所有的f\in X. 本文利用K-Carleson测度刻画了B_\log^\alpha(B_\log,0^\alpha)空间到Q_k(p, q)(Q_k, 0(p, q))空间的复合算子的有界性,以及B_\log^\alpha(B_\log,0^\alpha)空间到Q_k,0(p, q)空间的复合算子的有界性和紧性.

     

    Abstract: Suppose \phi is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator C_\phi: C_\phi(f)=f o \phi, for all f\in X. In this paper,we use K-carleson measure to discuss the bounded composition operators from B_\log^\alpha(B_\log,0^\alpha) to Q_k(p, q)(Q_k,0(p, q)) and the bounded and compact composition operators from B_\log^\alpha(B_\log,0^\alpha) to Q_k,0(p, q), where 0\alpha\infty.

     

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