APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

doi:10.1007/s10473-025-0521-z

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (5): 2208-2216.doi: 10.1007/s10473-025-0521-z

APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

Ali ABKAR

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran

收稿日期:2023-10-26 修回日期:2024-11-12 出版日期:2025-09-25 发布日期:2025-10-14

APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

Ali ABKAR

Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran

Received:2023-10-26 Revised:2024-11-12 Online:2025-09-25 Published:2025-10-14
About author:Ali Abkar, E-mail: abkar@sci.ikiu.ac.ir

摘要/Abstract

摘要： We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball. We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm; in particular, we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.

关键词: Bergman space, Besov space, dilation, weight function

Abstract: We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball. We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm; in particular, we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.

Key words: Bergman space, Besov space, dilation, weight function

中图分类号:

46E15

Ali ABKAR. APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL[J]. 数学物理学报(英文版), 2025, 45(5): 2208-2216.

Ali ABKAR. APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL[J]. Acta mathematica scientia,Series B, 2025, 45(5): 2208-2216.

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APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

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