Abstract
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.
Highlights
Let Ω be a bounded homogeneous domain in n
The composition operators as well as related operators known as the weighted composition operators between
Characterizations of the boundedness and the compactness of the composition operators and the weighted ones between the Bloch spaces were given in [10]-[12] for the polydisc case, and in [13]-[18] for the case of the bounded symmetric domains
Summary
Let Ω be a bounded homogeneous domain in n. The compactness of the composition operators for the weighted Bloch space on the bounded symmetric domains of RII ( p), RIII (q) is similar with the case of RI (m, n) ; we omit the details. Let φ be a holomorphic self-map of RI (m, n) and K a compact subset of RI (m, n) . there exists a constant C > 0 such that
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