Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc
Let Dn be the unit polydisc of ℂn, ϕ(z)=(ϕ1(z),…,ϕn(z)) be a holomorphic self-map of Dn, and ψ(z) a holomorphic function on Dn. Let H(Dn) denote the space of all holomorphic functions with domain Dn, H∞(Dn) the space of all bounded holomorphic functions on Dn, and B(Dn) the Bloch space, that is, B(D...
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Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/48478 |
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| author | Songxiao Li Stevo Stevic |
| author_facet | Songxiao Li Stevo Stevic |
| author_sort | Songxiao Li |
| collection | DOAJ |
| description | Let Dn be the unit polydisc of ℂn, ϕ(z)=(ϕ1(z),…,ϕn(z)) be a holomorphic self-map of Dn, and ψ(z) a holomorphic function on Dn. Let H(Dn) denote the space of all holomorphic functions with domain Dn, H∞(Dn) the space of all bounded holomorphic functions on Dn, and B(Dn) the Bloch space, that is, B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted
composition operator ψCϕ induced by ϕ(z) and ψ(z) to be bounded and compact from H∞(Dn) to the Bloch space B(Dn). |
| format | Article |
| id | doaj-art-1a9adf01a5d6403b90ca200ced09f50f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1a9adf01a5d6403b90ca200ced09f50f2025-08-20T03:54:21ZengWileyAbstract and Applied Analysis1085-33751687-04092007-01-01200710.1155/2007/4847848478Weighted Composition Operators from H∞ to the Bloch Space on the PolydiscSongxiao Li0Stevo Stevic1Department of Mathematics, Shantou University, Shantou, GuangDong 515063, ChinaMathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, SerbiaLet Dn be the unit polydisc of ℂn, ϕ(z)=(ϕ1(z),…,ϕn(z)) be a holomorphic self-map of Dn, and ψ(z) a holomorphic function on Dn. Let H(Dn) denote the space of all holomorphic functions with domain Dn, H∞(Dn) the space of all bounded holomorphic functions on Dn, and B(Dn) the Bloch space, that is, B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted composition operator ψCϕ induced by ϕ(z) and ψ(z) to be bounded and compact from H∞(Dn) to the Bloch space B(Dn).http://dx.doi.org/10.1155/2007/48478 |
| spellingShingle | Songxiao Li Stevo Stevic Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc Abstract and Applied Analysis |
| title | Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc |
| title_full | Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc |
| title_fullStr | Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc |
| title_full_unstemmed | Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc |
| title_short | Weighted Composition Operators from H∞ to the Bloch Space on the Polydisc |
| title_sort | weighted composition operators from h∞ to the bloch space on the polydisc |
| url | http://dx.doi.org/10.1155/2007/48478 |
| work_keys_str_mv | AT songxiaoli weightedcompositionoperatorsfromhtotheblochspaceonthepolydisc AT stevostevic weightedcompositionoperatorsfromhtotheblochspaceonthepolydisc |