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arXiv · 2311.15192

Complex symmetric weighted composition operators on the space $\mathcal{H}^2_2(\mathbb{D})$

Molla Basir Ahamed·Taimur Rahman
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Abstract

In this paper, we introduce a new norm for $\mathcal{S}^2(\mathbb{D})$, encompassing functions whose first and second derivatives belong to both the Hardy space $\mathcal{H}^2(\mathbb{D})$ and the classical Bergman space $\mathcal{A}^2(\mathbb{D})$. Moreover, we present some basic properties of the space $\mathcal{H}^2_2(\mathbb{D})$ and subsequently establish conditions for symbols $\phi$ and $\Psi$ to provide $W_{\Psi, \phi}$ complex symmetric, employing a unique conjugation $\mathcal{J}$.

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BibTeXRIS

Molla Basir Ahamed, Taimur Rahman. 2023-11-26. Complex symmetric weighted composition operators on the space $\mathcal{H}^2_2(\mathbb{D})$. https://arxiv.org/abs/2311.15192

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