Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces
Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator D φ , u n...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 211; H. 1; S. 222 - 233 |
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01.05.2009
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| Abstract | Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator
D
φ
,
u
n
(
f
)
(
z
)
=
u
(
z
)
f
(
n
)
(
φ
(
z
)
)
, where
u is a holomorphic function on the unit disk
D
,
φ is a holomorphic self-map of
D
and
n
∈
N
0
, from the mixed-norm space
H(
p,
q,
ϕ), where
p,
q
>
0 and
ϕ is normal, to the weighted-type space
H
μ
∞
or the little weighted-type space
H
μ
,
0
∞
. For the case of the weighted Bergman space
A
α
p
,
p
>
1, some bounds for the essential norm of the operator are also given. |
|---|---|
| AbstractList | Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator
D
φ
,
u
n
(
f
)
(
z
)
=
u
(
z
)
f
(
n
)
(
φ
(
z
)
)
, where
u is a holomorphic function on the unit disk
D
,
φ is a holomorphic self-map of
D
and
n
∈
N
0
, from the mixed-norm space
H(
p,
q,
ϕ), where
p,
q
>
0 and
ϕ is normal, to the weighted-type space
H
μ
∞
or the little weighted-type space
H
μ
,
0
∞
. For the case of the weighted Bergman space
A
α
p
,
p
>
1, some bounds for the essential norm of the operator are also given. |
| Author | Stević, Stevo |
| Author_xml | – sequence: 1 givenname: Stevo surname: STEVIC fullname: STEVIC, Stevo organization: Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 36/III, 11000 Beograd, Serbia |
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| Cites_doi | 10.1112/S0024610700008875 10.1155/2008/279691 10.1016/j.jmaa.2007.06.013 10.2307/2154848 10.2307/1971314 10.1155/2007/48478 10.1080/01630560701493222 10.1155/2007/28629 10.1080/01630560802282276 10.1016/j.amc.2008.09.002 10.1216/rmjm/1181069709 10.11650/twjm/1500574949 10.1016/j.jmaa.2008.03.063 10.4134/CKMS.2006.21.4.719 10.1155/2008/605807 10.1016/j.jmaa.2008.09.014 10.11650/twjm/1500405075 10.1016/j.amc.2008.10.032 10.1017/S0004972700038818 10.1080/17476930701754118 10.4171/ZAA/1301 10.1090/S0002-9939-02-06777-1 10.1155/JIA/2006/61018 10.1080/17476930701235225 10.1007/s00020-002-1203-y 10.1080/10652460701210250 10.1216/rmjm/1181075473 |
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| Keywords | Essential norm Weighted-type space Weighted differentiation composition operator Compactness Mixed-norm space Boundedness Multiplication Weighted differentiation composition Numerical analysis Applied mathematics Holomorphic mapping Integral transformation operator |
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| SubjectTerms | Boundedness Compactness Essential norm Exact sciences and technology Functional analysis Global analysis, analysis on manifolds Mathematical analysis Mathematics Mixed-norm space Numerical analysis Numerical analysis. Scientific computation Sciences and techniques of general use Several complex variables and analytic spaces Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Weighted differentiation composition operator Weighted-type space |
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