Norms and essential norms of composition operators from H ∞ to general weighted Bloch spaces in the polydisk

摘要

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