Bergman and Dirichlet spaces in the unit ball and symmetric lifting operator

Hassanlou, Mostafa; Abbasi, Ebrahim

doi:10.22060/ajmc.2022.21778.1107

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	Bergman and Dirichlet spaces in the unit ball and symmetric lifting operator
AUT Journal of Mathematics and Computing
مقاله 7، دوره 4، شماره 2، 2023، صفحه 155-160 اصل مقاله (358.34 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21778.1107
نویسندگان
Mostafa Hassanlou¹؛ Ebrahim Abbasi^* ²
¹Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran
²Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
چکیده
Let $\mathbb{B}_n$ be the open unit ball in $\mathbb{C}^n$ and $\mathbb{B}_n^2 = \mathbb{B}_n \times \mathbb{B}_n$. The symmetric lifting operator which lifts analytic functions from $H(\mathbb{B}_n)$ to $H(\mathbb{B}_n^2)$ is defined as follow \[ L(f)(z,w) = \frac{f(z) - f(w)}{z-w}. \] In this paper we investigate the action of symmetric lifting operator on the Bergman space in the unit ball. Also, we state a characterization for Dirichlet space and consider symmetric lifting operator on the Dirichlet space in the unit ball.
کلیدواژه‌ها
Symmetric lifting operator‎؛ Bergman space‎؛ Dirichlet space؛ ‎ Pseudo-hyperbolic metric

مراجع
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Bergman and Dirichlet spaces in the unit ball and symmetric lifting operator