Weighted Hardy and Cesaro operators on Heisenberg group and their norms

被引：6
作者：
Volosivets, S. S. [1 ]
机构：
[1] Saratov NG Chernyshevskii State Univ, Fac Mech & Math, Saratov, Russia
来源：
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2017年 / 28卷 / 12期
关键词：
Weighted Hardy operator; weighted Cesaro operator; Heisenberg group; Morrey space; Herz space; BLO space; HAUSDORFF OPERATORS; SPACES; BOUNDS; BMO; TRANSFORMS;
D O I：
10.1080/10652469.2017.1392946
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For weighted Hardy and Cesaro operators on Heisenberg group Hn, we give the exact values for its norms in Morrey space, its central variant and BLO(Hn). Also we prove the sharp two- sided estimate for its norm in Herz space. These statements are analogues of results due to Z. W. Fu and S. Z. Lu (Morrey and Herz spaces), S. S. Volosivets (BLO space) and generalize previous result concerning Lq(Hn) space by Chu et al.
引用
收藏
页码：940 / 952
页数：13
相关论文
共 23 条
  • [1] [Anonymous], 1982, Mathematical Notes
  • [2] Chu JY, 2016, J INEQUAL APPL, DOI 10.1186/s13660-016-1222-x
  • [3] ANOTHER CHARACTERIZATION OF BMO
    COIFMAN, RR
    ROCHBERG, R
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 79 (02) : 249 - 254
  • [4] About Riesz transforms on the Heisenberg groups
    Coulhon, T
    Muller, D
    Zienkiewicz, J
    [J]. MATHEMATISCHE ANNALEN, 1996, 305 (02) : 369 - 379
  • [5] Cui LH, 2005, SIBERIAN MATH J+, V46, P133
  • [6] Djrbashian M.M., 1968, IZV AKAD NAUK SSSR S, V32, P1075
  • [7] Edwards R. E., 1979, FOURIER SERIES MODER, V1
  • [8] Weighted Hardy operators and commutators on Morrey spaces
    Fu, Zunwei
    Lu, Shanzhen
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2010, 5 (03) : 531 - 539
  • [9] [FU Zunwei 傅尊伟], 2008, [数学进展, Advances in Mathematics], V37, P632
  • [10] Hausdorff Operators on the Heisenberg Group
    Guo, Jiu Hua
    Sun, Li Jing
    Zhao, Fa You
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2015, 31 (11) : 1703 - 1714
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