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