Norms and essential norms of composition operators from <b><it>H</it>^&#8734; </b>to general weighted Bloch spaces in the polydisk

Abstract

Abstract Let Un be the unit polydisk of ℂ n and φ a holomorphic self-map of Un. H∞(Un) and B log α ( U n ) denote the space of bounded holomorphic functions and the space of general weighted Bloch functions defined on Un, respectively, where α > 0. This paper gives some estimates of the norm and essential norm of the composition operator Cφ induced by φ from H∞(Un) to Blogα(Un) . As applications, some characterizations of the boundedness and compactness of Cφ from H∞(Un ) to Blogα(Un) are obtained. Moreover, we also characterize the weak compactness of the composition operator Cφ. MSC(2000): Primary 47B33; Secondary 32A37

Keywords

• Composition operator
• General weighted Bloch space
• Essential norm
• Boundedness
• Weak compactness