The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications. (English) Zbl 1131.47021
Summary: Let be the unit polydisc of be a holomorphic self-map of , and , , and denote the -Bloch space, little -Bloch space, and little star -Bloch space in the unit polydisc , respectively, where . This paper gives estimates of the essential norms of bounded composition operators induced by between or and or . As applications, some necessary and sufficient conditions for the (bounded) composition operators to be compact from or into or are obtained.
|32A18||Bloch functions, normal functions|
|46E15||Banach spaces of continuous, differentiable or analytic functions|