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Results in Mathematics

, 74:49 | Cite as

Commutators of Multi-sublinear Maximal Functions with Lipschitz Functions

  • Pu ZhangEmail author
Article
  • 13 Downloads

Abstract

Let \(0\le \alpha <mn\) and \(\mathcal {M}_{\alpha }\) be the multi-sublinear maximal function. For a collection of locally integrable functions \(\vec {b}=(b_1,\ldots ,b_m)\), we denote by \(\mathcal {M}_{\alpha ,\vec {b}}\) and \([\vec {b},\mathcal {M}_{\alpha }]\) the maximal and the nonlinear commutators of \(\mathcal {M}_{\alpha }\) with \(\vec {b}\). In this paper, we give some necessary and sufficient conditions for the boundedness of \(\mathcal {M}_{\alpha ,\vec {b}}\) and \([\vec {b},\mathcal {M}_{\alpha }]\) on the products of Lebesgue spaces when the symbols belong to Lipschitz spaces.

Keywords

Multi-sublinear maximal function maximal commutator nonlinear commutator Lipschitz space 

Mathematics Subject Classification

42B25 42B20 47B47 

Notes

Acknowledgements

The author would like to express his gratitude to the referee for his/her very valuable comments and kindly suggestion.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsMudanjiang Normal UniversityMudanjiangPeople’s Republic of China

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