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Abstract
Let be the class of all holomorphic functions on the unit ball
in
. For
with
and
an analytic self-map of
, the generalized composition operator is defined by
In this paper, we give estimates for the essential norms of the generalized composition operators
between Bloch-type spaces in terms of the powers of the components of
. We also give new characterizations for the boundedness and compactness of
between Bloch-type spaces.
AMS Subject Classifications:
Acknowledgements
The authors thank the editor and referee for useful comments and suggestions which improved the presentation of this paper.
Additional information
Funding
The work was supported in part by the National Natural Science Foundation of China [grant number 11371276], [grant number 11301373], [grant number 11226125].