Weighted composition operators between Bloch-type spaces in the polydisc

Abstract

For , let denote the -Bloch space on the unit polydisc of and a holomorphic self-map of . We investigate the boundedness and compactness of the weighted composition between -Bloch space (little -Bloch space ) and -Bloch space (little -Bloch space ). The most important result in the paper is that conditions for the compactness are different for the cases and , unlike for the case of the weighted operators on the unit disc. Bibliography: 32 titles.