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The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications
Journal of Inequalities and Applications volume 2006, Article number: 90742 (2006)
Abstract
Let be the unit polydisc of
and
a holomorphic self-map of
.
,
and
denote the
-Bloch space, little
-Bloch space, and little star
-Bloch space in the unit polydisc
, respectively, where
. This paper gives the estimates of the essential norms of bounded composition operators
induced by
between
(
or
) and
(
or
). As their applications, some necessary and sufficient conditions for the (bounded) composition operators
to be compact from
(
or
) into
(
or
) are obtained.
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Zhou, Z., Liu, Y. The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications. J Inequal Appl 2006, 90742 (2006). https://doi.org/10.1155/JIA/2006/90742
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Keywords
- Composition Operator
- Bloch Space
- Essential Norm
- Bound Composition Operator
- Unit Polydisc