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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| Vydáno v: | Applied mathematics and computation Ročník 211; číslo 1; s. 222 - 233 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier Inc
01.05.2009
Elsevier |
| Témata: | |
| ISSN: | 0096-3003, 1873-5649 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
|---|---|
| ISSN: | 0096-3003 1873-5649 |
| DOI: | 10.1016/j.amc.2009.01.061 |