Norms and essential norms of composition operators from H∞to general weighted Bloch spaces in the polydisk
Let U n be the unit polydisk of ℂ n and φ a holomorphic self-map of U n . H ∞ ( U n ) and B log α ( U n ) denote the space of bounded holomorphic functions and the space of general weighted Bloch functions defined on U n , respectively, where α > 0. This paper gives some estimates of the norm and...
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| Veröffentlicht in: | Journal of inequalities and applications 2011-09, Vol.2011 (1), p.46-46, Article 46 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
U
n
be the unit polydisk of
ℂ
n
and
φ
a holomorphic self-map of
U
n
.
H
∞
(
U
n
) and
B
log
α
(
U
n
)
denote the space of bounded holomorphic functions and the space of general weighted Bloch functions defined on
U
n
, respectively, where
α
>
0. This paper gives some estimates of the norm and essential norm of the composition operator
C
φ
induced by
φ
from
H
∞
(
U
n
) to
B
log
α
(
U
n
)
. As applications, some characterizations of the boundedness and compactness of
C
φ
from
H
∞
(
U
n
) to
B
log
α
(
U
n
)
are obtained. Moreover, we also characterize the weak compactness of the composition operator
C
φ
.
MSC(2000):
Primary 47B33; Secondary 32A37 |
|---|---|
| ISSN: | 1029-242X 1025-5834 1029-242X |
| DOI: | 10.1186/1029-242X-2011-46 |