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Characterization of boundedness of some commutators of maximal functions in terms of Lipschitz spaces

  • Pu Zhang
Article

Abstract

We give some characterizations of the boundedness of the maximal or nonlinear commutators of the Hardy–Littlewood maximal function and sharp maximal function in variable exponent Lebesgue spaces when the symbols b belong to the Lipschitz spaces, by which some new characterizations of Lipschitz spaces and nonnegative Lipschitz functions are obtained. Some equivalent relations between the Lipschitz norm and the variable exponent Lebesgue norm are also given.

Keywords

Hardy–Littlewood maximal function Sharp maximal function Fractional maximal function Commutator Lipschitz space Variable exponent Lebesgue space 

Mathematics Subject Classification

47B47 42B25 46E30 42B20 42B35 26A16 

Notes

Acknowledgements

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

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

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

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