Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (1): 56-67.

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Boundedness of Generalized Higher Order Commutators of Marcinkiewicz |Integrals with Variable Kernels on Herz-type Hardy Spaces

 MO Hui-Xia1, LU Shan-Zhen2   

  1. 1. School of Science, Beijing University of Post and Telecommunications, Beijing 100876 2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875
  • Received:2013-07-15 Revised:2014-11-24 Online:2015-02-25 Published:2015-02-25

Abstract:

Let  be a function with derivatives of order  and  The authors in the
paper prove that if  is homogenous of degree zero  and satisfies the mean value zero condition about the variable , then both the generalized higher order Marcinkiewicz  integral and itsvariationare bounded on Herz-type Hardy spaces.

 

Key words: Marcinkiewicz type integral ,  Herz-type Hardy space ,  Space of Lipschitz functions ,  Commutator

CLC Number: 

  • 42B20
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