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

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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.

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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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  1. Department of Mathematics, Mudanjiang Normal University, Mudanjiang, 157011, People’s Republic of China

    Pu Zhang

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  1. Pu Zhang
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Correspondence to Pu Zhang.

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Supported by National Natural Science Foundation of China (Grant Nos. 11571160 and 11471176).

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Zhang, P. Characterization of boundedness of some commutators of maximal functions in terms of Lipschitz spaces. Anal.Math.Phys. 9, 1411–1427 (2019). https://doi.org/10.1007/s13324-018-0245-5

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