Norms and essential norms of composition operators from H^sup â z^to general weighted Bloch spaces in the polydisk

Let U ^sup n^be the unit polydisk of [InlineEquation not available: see fulltext.] and Ï[dagger] a holomorphic self-map of U ^sup n^. H ^sup â z^(U ^sup n^) and [InlineEquation not available: see fulltext.] denote the space of bounded holomorphic functions and the space of general weighted Bloch functions defined on U ^sup n^, respectively, where α > 0. This paper gives some estimates of the norm and essential norm of the composition operator C ^sub Ï[dagger]^induced by Ï[dagger] from H ^sup â z^(U ^sup n^) to [InlineEquation not available: see fulltext.]. As applications, some characterizations of the boundedness and compactness of C ^sub Ï[dagger]^from H ^sup â z^(U ^sup n^ ) to [InlineEquation not available: see fulltext.] are obtained. Moreover, we also characterize the weak compactness of the composition operator C ^sub Ï[dagger]^. MSC(2000): Primary 47B33; Secondary 32A37[PUBLICATION ABSTRACT]