Composition-Differentiation Operator on Weighted Bergman Spaces

2023/01/20 by Vasudevarao Allu, Allu, Vasudevarao, Himadri Halder +3
Mathematics · #30H20 #47A05 #47B15 #47B33 #47B38 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2301.08575

openalex publication_date 2023/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the complex symmetry of weighted composition-differentiation operator D_{n, ψ, ϕ} on weighted Bergman spaces A²_α with respect to the conjugation C_{μ, η} for μ, η∈ \z∈ ℂ:|z|=1\. We obtain explicit conditions for which the operator D_{n, ψ, ϕ} is Hermitian and normal. We also characterize the complex symmetric weighted composition-differentiation operator for derivative Hardy spaces.

Related

• Complex symmetric Weighted Composition--Differentiation Operators of order n on the Weighted Bergman Spaces
• Complex symmetric weighted Composition Differentiation Operators
• Generalized weighted composition-differentiation operators on weighted Bergman spaces
• Generalized weighted composition operators on Hardy space H²(\mathbbDⁿ)
• Weighted Composition--Differentiation Operator on the Hardy and Weighted Bergman Spaces