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

	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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