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Published in:
Open Access 01-12-2006 | Research Article
Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball
Published in: Journal of Inequalities and Applications | Issue 1/2006
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Abstract
For
, let
and
denote, respectively, the
-Bloch and holomorphic
-Lipschitz spaces of the open unit ball
in
. It is known that
and
are equal as sets when
. We prove that these spaces are additionally norm-equivalent, thus extending known results for
and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator
from
to
.
, let
and
denote, respectively, the
-Bloch and holomorphic
-Lipschitz spaces of the open unit ball
in
. It is known that
and
are equal as sets when
. We prove that these spaces are additionally norm-equivalent, thus extending known results for
and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator
from
to
.