数学理论与应用 ›› 2023, Vol. 43 ›› Issue (2): 107-121.doi: 10.3969/j.issn.1006­8074.2023.02.008

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变指标有界变差空间的准紧集

司亚楠, 徐景实*   

  1. 桂林电子科技大学数学与计算科学学院, 桂林, 541004
  • 出版日期:2023-06-28 发布日期:2023-06-27
  • 通讯作者: Xu Jingshi (1966–), Associate Professor, PhD; E-mail: jingshixu@126.com E-mail:jingshixu@126.com

Precompact Sets in Variable Exponent Bounded Variation Spaces

Si Yanan, Xu Jingshi*   

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology,\\ Guilin 541004, China
  • Online:2023-06-28 Published:2023-06-27
  • Supported by:
    This work is supported by National Natural Science Foundation of China (No. 12161022)

摘要: 本文利用等度变差集, 考虑单变量和双变量情形下变指标Banach空间值的有界Wiener变差空间和有界Riesz变差空间中准紧集的充分条件.

关键词: 准紧集, 有界变差空间, 变指标, Banach空间值

Abstract: By equivariated sets, we consider sufficient conditions for precompact sets in variable exponent Banach space-valued bounded Wiener variation spaces and bounded Riesz variation spaces in univariate and bivariate cases, respectively.

Key words: Precompact set, Bounded variation space, Variable exponent, Banach space-valued