COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL
Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition...
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| Published in | Acta mathematica scientia Vol. 29; no. 5; pp. 1430 - 1438 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2009
Department of Mathematics, University of Science and Technology of China, Hefei 230026, China%Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(09)60115-6 |
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| Abstract | Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained. |
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| AbstractList | Let φ be a holomorphic self-map of
B
n
and ψ ∈
H(
B
n
). A composition type operator is defined by
T
ψ,φ(
f)= ψ
f o φ for
f ∈
H(
B
n
), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator
T
ψ,φ to be bounded or compact from Hardy space
H
p
(
B
n
) to μ-Bloch space
B
μ(
B
n
). The conditions are some supremums concerned with ψ, φ, their derivatives and Bergman metric of
B
n
. At the same time, two corollaries are obtained. Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,φ to be bounded or compact from Hardy space HP（Bn） to μ-Bloch space Bμ（Bn）. The conditions are some supremums concerned with ψ,φ, their derivatives and Bergman metric of Bn. At the same time, two corollaries are obtained. O1; Let be a holomorphic self-map of B_n and ψ∈ H(B_n). A composition type operator is defined by T_(ψ,(ψ)) (f)=ψf ο(ψ) for f ∈ H(B_n), which is a generalization of the multiplication operator and the composition operator. In this article, the necessary and sufficient conditions are given for the composition type operator Tψ,(ψ) to be bounded or compact from Hardy space H~p(B_n) to μ-Bloch space B_μ(B_n). The conditions are some supremums concerned with ψ,(ψ), their derivatives and Bergman metric of B_n. At the sametime, two corollaries are obtained. |
| Author | 王雄亮 刘太顺 |
| AuthorAffiliation | Department of Mathematics, University of Science and Technology of China, Hefei 230026, China Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China |
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| Cites_doi | 10.2307/2154848 10.1016/j.jmaa.2004.06.033 10.1007/s101149900028 10.1006/jmaa.1999.6341 10.1090/S0002-9939-1993-1152987-6 10.1216/rmjm/1181069993 10.1007/s00013-002-8252-y 10.1080/17476930108815401 10.4153/CMB-2008-021-2 |
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| Copyright | 2009 Wuhan Institute of Physics and Mathematics Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | 42B30 μ-Bloch spaces Hardy spaces compactness 47B33 boundedness 30D45 composition type operators |
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| Notes | Hardy spaces; μ-Bloch spaces; composition type operators; boundedness; compactness μ-Bloch spaces Hardy spaces compactness 42-1227/O S968.22 O177.3 boundedness composition type operators |
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| Snippet | Let φ be a holomorphic self-map of Bn and ψ ∈ H（Hn）. A composition type operator is defined by Tψ,φ（f） = ψf o φ for f ∈ H（Bn）, which is a generalization of the... Let φ be a holomorphic self-map of B n and ψ ∈ H( B n ). A composition type operator is defined by T ψ,φ( f)= ψ f o φ for f ∈ H( B n ), which is a... O1; Let be a holomorphic self-map of B_n and ψ∈ H(B_n). A composition type operator is defined by T_(ψ,(ψ)) (f)=ψf ο(ψ) for f ∈ H(B_n), which is a... |
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| SubjectTerms | 30D45 42B30 47B33 Bloch空间 boundedness compactness composition type operators Hardy spaces Hardy空间 μ-Bloch spaces 充分条件 单位球 德州仪器 组合型 组成型 经营者 |
| Title | COMPOSITION TYPE OPERATORS FROM HARDY SPACES TO μ-BLOCH SPACES ON THE UNIT BALL |
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