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

Stevo Stević and Sei-Ichiro Ueki

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: 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.

Date: 2010
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https://doi.org/10.1155/2010/214762

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:214762

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