MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE*

doi:10.1007/s10473-023-0516-6

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (5): 2204-2214.doi: 10.1007/s10473-023-0516-6

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*

Ali Abkar

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

收稿日期:2021-10-09 修回日期:2022-11-02 发布日期:2023-10-25

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*

Ali Abkar

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

Received:2021-10-09 Revised:2022-11-02 Published:2023-10-25
About author:Ali Abkar, E-mail: abkar@sci.ikiu.ac.ir

摘要/Abstract

摘要： We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman, weighted Dirichlet, and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.

关键词: mean approximation, dilatation, non-radial weight, angular weight, weighted Bergman space, weighted Besov space

Abstract: We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman, weighted Dirichlet, and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.

Key words: mean approximation, dilatation, non-radial weight, angular weight, weighted Bergman space, weighted Besov space

中图分类号:

46E15

Ali Abkar. MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*[J]. 数学物理学报(英文版), 2023, 43(5): 2204-2214.

Ali Abkar. MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*[J]. Acta mathematica scientia,Series B, 2023, 43(5): 2204-2214.

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MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE^*

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