Weighted Composition Operators between different Bloch-type Spaces in Polydisk

2005/03/27 by Ze‐Hua Zhou, Zehua Zhou, Zhou, Zehua
Mathematics · #32A30 #32A37 #47B33 #47B38 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32A30 #msc:32A37 #msc:47B33 #msc:47B38

paper · pdf · doi:10.48550/arxiv.math/0503622

27 Pages

openalex publication_date 2005/03/27 · arxiv created 2005/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ϕ(z)=(ϕ₁(z), ...,ϕ_n(z)) be a holomorphic self-map of Uⁿ and ψ(z) a holomorphic function on Uⁿ, where Uⁿ is the unit polydisk of \Bbb Cⁿ. Let p≥ 0, q≥ 0, this paper gives some necessary and sufficient conditions for the weighted composition operator W_ψ,ϕ induced by ψ and ϕ to be bounded and compact between p-Bloch space \cal B^p(Uⁿ) and q-Bloch space \cal B^q(Uⁿ).

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