Points of monotonicity in F-normed Orlicz function spaces

被引：2
作者：
Yang, Yabo [1 ]
Cui, Yunan [1 ]
Kaczmarek, Radoslaw [2 ]
机构：
[1] Harbin Univ Sci & Technol, Dept Math, Harbin 150080, Peoples R China
[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, Uniwersytetu Poznanskiego 4, PL-61614 Poznan, Poland
来源：
AEQUATIONES MATHEMATICAE | 2023年 / 97卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Orlicz space; Mazur-Orlicz F-norm; Points of lower (upper) strict monotonicity; Points of lower (upper) local uniform monotonicity; APPROXIMATION; L(INFINITY); COPIES;
D O I：
10.1007/s00010-023-00961-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper points of lower strict monotonicity, upper strict monotonicity, lower local uniform monotonicity and upper local uniform monotonicity of Orlicz function spaces equipped with a Mazur-Orlicz F-norm and generated by a monotone (non-convex in general) Orlicz function are studied. We show that both the necessary and sufficient conditions and the suitable theorems are formulated in full generality. Moreover, lower (upper) strict monotonicity and lower (upper) local uniform monotonicity theorems of the paper are revealed as corollaries in this paper.
引用
收藏
页码：659 / 682
页数：24
相关论文
共 19 条
  • [1] Bai X., 2020, J FUNCT SPACES, V2020, P1
  • [2] Chen S., 1996, GEOMETRY ORLICZ SPAC, V356, P1
  • [3] Monotonicity and best approximation in Banach lattices
    Chen, Shu Tao
    He, Xin
    Hudzik, H.
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2009, 25 (05) : 785 - 794
  • [4] Isometric copies of l1 and l∞ in Orlicz spaces equipped with the Orlicz norm
    Chen, ST
    Cui, YN
    Hudzik, H
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (02) : 473 - 480
  • [5] Criteria for monotonicity properties of Musielak-Orlicz spaces equipped with the Amemiya norm
    Cui, Y
    Hudzik, H
    Szymaszkiewicz, L
    Wang, T
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) : 376 - 390
  • [6] Uniform monotonicity of Orlicz spaces equipped with the Mazur-Orlicz F-norm and dominated best approximation in F-normed Kothe spaces
    Cui, Yunan
    Hudzik, Henryk
    Kaczmarek, Radoslaw
    Kolwicz, Pawel
    [J]. MATHEMATISCHE NACHRICHTEN, 2022, 295 (03) : 487 - 511
  • [7] Geometric properties of F-normed Orlicz spaces
    Cui, Yunan
    Hudzik, Henryk
    Kaczmarek, Radoslaw
    Kolwicz, Pawel
    [J]. AEQUATIONES MATHEMATICAE, 2019, 93 (01) : 311 - 343
  • [8] Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices
    Hudzik, H
    Kurc, W
    [J]. JOURNAL OF APPROXIMATION THEORY, 1998, 95 (03) : 353 - 368
  • [9] Points of monotonicity in Musielak-Orlicz function spaces endowed with the Luxemburg norm
    Hudzik, H
    Liu, XB
    Wang, TF
    [J]. ARCHIV DER MATHEMATIK, 2004, 82 (06) : 534 - 545
  • [10] Hudzik H, 2019, POSITIVITY, V23, P941, DOI 10.1007/s11117-019-00645-9
12