Complex symmetric weighted composition operators on the space H²₂(\mathbbD)

2023/11/26 by Molla Basir Ahamed, Ahamed, Molla Basir, Taimur Rahman +1
Mathematics · #30H10 #30H50 #30J10 #47B33 #47B38 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2311.15192

openalex publication_date 2023/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a new norm for S²(\mathbbD), encompassing functions whose first and second derivatives belong to both the Hardy space H²(\mathbbD) and the classical Bergman space A²(\mathbbD). Moreover, we present some basic properties of the space H²₂(\mathbbD) and subsequently establish conditions for symbols ϕ and Ψ to provide W_{Ψ, ϕ} complex symmetric, employing a unique conjugation J.

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