Abstract and Applied Analysis

On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

Stevo Stević and Sei-Ichiro Ueki

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Abstract

Let 𝔹 denote the open unit ball of n . 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: I φ g f ( z ) = 0 1 f ( φ ( t z ) ) g ( t z ) ( d t / t ) , z 𝔹 . Here f denotes the radial derivative of a holomorphic function f in 𝔹 . We study the boundedness and compactness of the operator between Bloch-type spaces ω and μ , where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ω , 0 and μ , 0 .

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 214762, 14 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620729

Digital Object Identifier
doi:10.1155/2010/214762

Mathematical Reviews number (MathSciNet)
MR2660388

Zentralblatt MATH identifier
1200.32005

Citation

Stević, Stevo; Ueki, Sei-Ichiro. On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball. Abstr. Appl. Anal. 2010 (2010), Article ID 214762, 14 pages. doi:10.1155/2010/214762. https://projecteuclid.org/euclid.aaa/1288620729


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