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

Hassanlou, Mostafa; Abbasi, Ebrahim

doi:10.22060/ajmc.2022.21778.1107

دانشگاه صنعتی امیرکبیر

تعداد نشریات	8
تعداد شماره‌ها	414
تعداد مقالات	5,478
تعداد مشاهده مقاله	6,010,333
تعداد دریافت فایل اصل مقاله	5,299,916

	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
[1] P. Duren and A. Schuster, Bergman spaces, vol. 100 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2004. [2] M. Hassanlou and M. Sohrabi, Characterization of Bloch type spaces and symmetric lifting operator, International Journal of Nonlinear Analysis and Applications, (2022). [3] M. Hassanlou and H. Vaezi, Double integral characterization for Bergman spaces, Iran. J. Math. Sci. Inform., 11 (2016), pp. 27–34, 148. [4] H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, vol. 199 of Graduate Texts in Mathematics, Springer-Verlag, New York, 2000. [5] S. Li, H. Wulan, R. Zhao, and K. Zhu, A characterisation of Bergman spaces on the unit ball of C n, Glasg. Math. J., 51 (2009), pp. 315–330. [6] S. Li, H. Wulan, and K. Zhu, A characterization of Bergman spaces on the unit ball of C n. II, Canad. Math. Bull., 55 (2012), pp. 146–152. [7] M. Stessin and K. Zhu, Composition operators on embedded disks, J. Operator Theory, 56 (2006), pp. 423–449. [8] H. Wulan and K. Zhu, Lipschitz type characterizations for Bergman spaces, Canad. Math. Bull., 52 (2009), pp. 613–626. [9] K. Zhu, Spaces of holomorphic functions in the unit ball, vol. 226 of Graduate Texts in Mathematics, Springer[1]Verlag, New York, 2005.
آمار تعداد مشاهده مقاله: 724 تعداد دریافت فایل اصل مقاله: 402

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

آمار

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