ON THE INTEGRABILITY AND UNIFORM CONVERGENCE OF MULTIPLICATIVE FOURIER TRANSFORMS

被引：0
|
作者：
Golubov, Boris I. [1 ]
Volosivets, Sergey S. [2 ]
机构：
[1] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Region, Russia
[2] Saratov NG Chernyshevskii State Univ, Dept Mech & Math, Saratov 410028, Russia
来源：
GEORGIAN MATHEMATICAL JOURNAL | 2009年 / 16卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Multiplicative Fourier transform; integrability; uniform convergence; Nikol'skii type inequality; SERIES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Analogues of two Hardy-Littlewood theorems are proved for a multiplicative Fourier transform. A Szasz type condition for a multiplicative Fourier transform is given and its nonimprovability is proved. Besides, an analogue of Ul'yanov's theorem on the uniform convergence of a trigonometric series and an analogue of Konyuskov-Stechkin's embedding theorem are obtained by means of a Nikol'skii type inequality of various metrics.
引用
收藏
页码：533 / 546
页数：14
相关论文
共 50 条
  • [1] Uniform convergence and integrability of multiplicative Fourier transforms
    Volosivets, S. S.
    Golubov, B. I.
    MATHEMATICAL NOTES, 2015, 98 (1-2) : 53 - 67
  • [2] Uniform convergence and integrability of multiplicative Fourier transforms
    S. S. Volosivets
    B. I. Golubov
    Mathematical Notes, 2015, 98 : 53 - 67
  • [3] Integrability and Uniform Convergence of Multiplicative Transforms
    Golubov, B. I.
    Volosivets, S. S.
    NEW TRENDS IN ANALYSIS AND INTERDISCIPLINARY APPLICATIONS, 2017, : 363 - 369
  • [4] Weighted Integrability of Multiplicative Fourier Transforms
    Volosivets, S. S.
    Golubov, B. I.
    PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2010, 269 (01) : 65 - 75
  • [5] Weighted integrability of multiplicative Fourier transforms
    S. S. Volosivets
    B. I. Golubov
    Proceedings of the Steklov Institute of Mathematics, 2010, 269 : 65 - 75
  • [6] Weighted Integrability of Multiple Multiplicative Fourier Transforms
    Volosivets, S. S.
    Golubov, B., I
    MATHEMATICAL NOTES, 2022, 111 (3-4) : 364 - 372
  • [7] Weighted Integrability of Multiple Multiplicative Fourier Transforms
    S. S. Volosivets
    B. I. Golubov
    Mathematical Notes, 2022, 111 : 364 - 372
  • [8] Uniform convergence and integrability of Fourier integrals
    Dyachenko, Mikhail
    Liflyand, Elijah
    Tikhonov, Sergey
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 372 (01) : 328 - 338
  • [9] UNIFORM CONVERGENCE OF FOURIER TRANSFORMS ON GROUPS
    GEORGAKIS, C
    ACTA SCIENTIARUM MATHEMATICARUM, 1970, 31 (3-4): : 359 - +
  • [10] On Uniform Convergence of Transformations of Fourier Series on Multiplicative Systems
    Agafonova, N. Y.
    IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2009, 9 (01): : 3 - 8
12345