Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 597-610.

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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)

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

CLC Number: 

  • O174.2
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