Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (6): 1606-1615.

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Commutators of Weighted Composition Operators on Hardy Space of the Unit Ball

Ning Xu1(),Zehua Zhou2,*(),Ying Ding1   

  1. 1 School of Science, Jiangsu Ocean University, Jiangsu Lianyungang 222005
    2 Department of Mathematics, Tianjin University, Tianjin 300072
  • Received:2020-06-04 Online:2021-12-26 Published:2021-12-02
  • Contact: Zehua Zhou;
  • Supported by:
    the NSFC(11771323);the Doctoral Research Launch Fund of Jiangsu Ocean University(KQ17006)


In this paper, we study commutators of weighted composition operators with linear fractional non-automorphisms on Hardy space of the unit ball. First, we obtain the formula of commutators of weighted composition operators. Then, we characterize compactness of commutators according to two special situations of linear fractional maps. Finally, we obtain that commutators are compact when linear fractional maps are parabolic and commutators are not compact when linear fractional maps are hyperbolic.

Key words: Hardy spaces, Weighted composition operators, Commutators

CLC Number: 

  • O177.2