APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL

  • Ali ABKAR
Expand
  • Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34149, Iran
Ali Abkar, E-mail: abkar@sci.ikiu.ac.ir

Received date: 2023-10-26

  Revised date: 2024-11-12

  Online published: 2025-10-14

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.

Cite this article

Ali ABKAR . APPROXIMATION IN WEIGHTED HOLOMORPHIC BESOV SPACES ON POLYDISK AND UNIT BALL[J]. Acta mathematica scientia, Series B, 2025 , 45(5) : 2208 -2216 . DOI: 10.1007/s10473-025-0521-z

References

[1] Abkar A. Mean approximation in Bergman spaces of polyanalytic functions. Anal Math Phys, 2022, 12: Art 52
[2] Abkar A. Approximation in weighted analytic Besov spaces and in generalized Fock spaces. Complex Anal Oper Theory, 2022, 16(11): 1-19
[3] Abkar A. Non-radial weights and polynomial approximation in spaces of analytic functions. Complex Variables and Elliptic Equations, 2024, 69: 107-121
[4] Abkar A. Mean approximation by dilatations in Bergman spaces on the upper half-plane. Acta Math Sci, 2023, 43B: 2204-2214
[5] Cao G, He L, Zhu K. Polynomial approximation and composition operators. Proc Amer Math Soc, 2021, 149: 3715-3724
[6] Carleman T. Über die approximation analytischer funktionen durch lineare Aggregate von vorgegebenen Potenzen. Ark Mat Astr Fys, 1923, 17: 1-30
[7] Farrell O J. On approximation to an analytic function by polynomials. Bull Amer Math Soc, 1934, 40: 908-914
[8] Farrell O J. On approximation by polynomials to a function analytic in a simply connected region. Bull Am Math Soc, 1935, 41: 707-711
[9] Hedberg L I. Approximation in the mean by analytic functions. Trans Amer Math Soc, 1972, 163: 157-171
[10] Hedberg L I. Weighted mean approximation in Carathéodory domains. Math Scand, 1968, 23: 113-122
[11] Korhonen T, Rättyä J. Zero sequences, factorization and sampling measures for weighted Bergman spaces. Mathematische Zeitschrift, 2019, 291: 1145-1173
[12] Mergelyan S N. On the completeness of systems of analytic functions. Amer Math Soc Transl, 1962, 19: 109-136
[13] Park I, Zhao J, Zhu K. Norm approximation by Taylor polynomials in Hardy and Bergman spaces. Internat J Math, 2021, 32(6): Art 2150037
[14] Peláez J A, Rättya J. Weighted Bergman Spaces Induced by Rapidly Increasing Weights. Providence, RI: American Mathematical Society, 2014
[15] Royden H L. Real Analysis.New Jersey: Prentice-Hall, 1988
[16] Yeh J.Real Analysis: Theory of Measure and Integration. Singapore: World Scientific, 1988
[17] Zhu K.Spaces of Holomorphic Functions in the Unit Ball. New York: Springer-Verlag, 2005
Options
Outlines

/