The Essential Norm of Composition Operator between Generalized Bloch Spaces in Polydiscs and its Applications
نویسندگان
چکیده
Let U be the unit polydisc of C n and φ = (φ1, . . . , φn) a holomorphic self-map of U. By Bp(Un), B 0 (U) and B 0∗ (U) denote the p-Bloch space, Little p-Bloch space and Little star p-Bloch space in the unit polydisc U respectively, where p, q > 0. This paper gives the estimates of the essential norms of bounded composition operators Cφ induced by φ between Bp(Un) (B 0(Un) or B 0∗(Un) ) and Bq(Un) (B 0(Un) or B 0∗ (U)). As their applications, some necessary and sufficient conditions for the bounded composition operators Cφ to be compact from Bp(Un) (B 0(U) or B 0∗(U)) into Bq(Un) (B 0 (U) or B 0∗ (U)) are obtained.
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