数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 597-610.

• 论文 • 上一篇    下一篇

Marcinkiewicz积分算子及其交换子在非齐度量测度空间上的有界性

韩瑶瑶(),赵凯*()   

  1. 青岛大学数学与统计学院 山东青岛 266071
  • 收稿日期:2019-08-27 出版日期:2020-06-26 发布日期:2020-07-15
  • 通讯作者: 赵凯 E-mail:hanyaoyao@aliyun.com;zhkzhc@aliyun.com
  • 作者简介:韩瑶瑶, E-mail:hanyaoyao@aliyun.com
  • 基金资助:
    国家自然科学基金(11471176);国家自然科学基金(11871293)

Boundedness of Marcinkiewicz Integral and Its Commutator on Non-Homogeneous Metric Measure Spaces

Yaoyao Han(),Kai Zhao*()   

  1. School of Mathematics and Statistics, Qingdao University, Shandong Qingdao 266071
  • Received:2019-08-27 Online:2020-06-26 Published:2020-07-15
  • Contact: Kai Zhao E-mail:hanyaoyao@aliyun.com;zhkzhc@aliyun.com
  • Supported by:
    the NSFC(11471176);the NSFC(11871293)

摘要:

$ ({\cal X}, d, \mu) $是一个满足上双倍条件和几何双倍条件的非齐度量测度空间.利用非齐度量测度空间的一些特征和不等式技巧,证明了Marcinkiewicz积分算子及其交换子在非齐度量测度空间上的Herz空间以及Herz型Hardy空间上的有界性.

关键词: 非齐度量测度空间, Herz空间, Hardy空间, Marcinkiewicz积分算子, 有界性

Abstract:

Let $ ({\cal X}, d, \mu) $ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling conditions. By using the properties of non-homogeneous metric measure space and inequality technique, the authors proved that the Marcinkiewicz integral operator and its commutator are bounded on Herz spaces and Herz type Hardy spaces with non-homogeneous metric measure space.

Key words: Non-homogeneous metric measure space, Herz space, Hardy space, Marcinkiewicz integral, Boundedness

中图分类号: 

  • O174.2