On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball
Let 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a hol...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/214762 |
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| author | Stevo Stević Sei-Ichiro Ueki |
| author_facet | Stevo Stević Sei-Ichiro Ueki |
| author_sort | Stevo Stević |
| collection | DOAJ |
| description | Let 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a holomorphic function f in 𝔹. We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0. |
| format | Article |
| id | doaj-art-397e92fe9e6f4417898f5c7b11cf1578 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-397e92fe9e6f4417898f5c7b11cf15782025-02-03T06:11:38ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/214762214762On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit BallStevo Stević0Sei-Ichiro Ueki1Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, SerbiaFaculty of Engineering, Ibaraki University, Hitachi 316-8511, JapanLet 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0)=0, we define the following integral-type operator: Iφgf(z)=∫01ℜf(φ(tz))g(tz)(dt/t), z∈𝔹. Here ℜf denotes the radial derivative of a holomorphic function f in 𝔹. We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0.http://dx.doi.org/10.1155/2010/214762 |
| spellingShingle | Stevo Stević Sei-Ichiro Ueki On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball Abstract and Applied Analysis |
| title | On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball |
| title_full | On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball |
| title_fullStr | On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball |
| title_full_unstemmed | On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball |
| title_short | On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball |
| title_sort | on an integral type operator acting between bloch type spaces on the unit ball |
| url | http://dx.doi.org/10.1155/2010/214762 |
| work_keys_str_mv | AT stevostevic onanintegraltypeoperatoractingbetweenblochtypespacesontheunitball AT seiichiroueki onanintegraltypeoperatoractingbetweenblochtypespacesontheunitball |