Composition operators between p-Bloch space and q-Bloch space in the unit ball

Abstract

Let B_n be the unit ball of C ⁿ and ø = ø₁ … ø _n a holomorphic self-map of B _n . The main purpose of this paper is to discuss the boundedness and compactness of composition operator C_ø between p-Bloch space β^p B_n and q-Bloch space β^qB_n … wherep p ⩾0 and q⩾0.

Keywords:

• p-Bloch space
• automorphisms
• composition operator

Supported by the National Natural Science Foundation of China (Grand No. 10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University.

Supported by the National Natural Science Foundation of China (Grand No. 10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University.

Notes

Supported by the National Natural Science Foundation of China (Grand No. 10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University.