Bergman空间上复合算子的下有界性

Bounded Below Property of Composition Operator on Bergman Space

关键词:  Bergman空间  复合算子  下有界性

Key words:  Bergman space  composition operator  bounded below property

摘要:

给出Bergman空间L_a^p(Ω)={f∈H(Ω):||f||=∫_Ω|f(x)|^pdm(x))^1/p<∞}上复合算子下有界的一个充分条件φ(Ω)=Ω,sup_z∈Ω│detJ_φ(z)│<∞,和一个必要条件φ(Ω)=Ω,其中φ是Ω到自身的解析映射.

Abstract:

In this paper, we give a sufficient condition φ (Ω)=Ω, sup_z∈Ω|detJ_φ (z)|<∞, and a necessary condition φ (Ω)=Ω for bounded below of composition operator on Bergman space L_a^p (Ω)={f∈H (Ω):‖f‖= (∫_Ω|f (x)|^pdm (x))^1/p<∞}.