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Characterization of Lipschitz Functions via the Commutators of Singular and Fractional Integral Operators in Variable Lebesgue Spaces

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Abstract

We obtain characterizations of a variable version of Lipschitz spaces in terms of the boundedness of commutators of Calderón-Zygmund and fractional type operators in the context of the variable exponent Lebesgue spaces L p(⋅), where the symbols of the commutators belong to the Lipschitz spaces. A useful tool is a pointwise estimate involving the sharp maximal operator of the commutator and certain associated maximal operators, which is new even in the classical context. Some boundedness properties of the commutators between Lebesgue and Lipschitz spaces in the variable context are also proved.

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Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ingeniería Química (UNL), Santa Fe, Argentina

    G. G. Pradolini

  2. Departamento de Matemática (FaCENA-UNNE), CONICET, Corrientes, Argentina

    W. A. Ramos

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  1. G. G. Pradolini
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  2. W. A. Ramos
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Correspondence to W. A. Ramos.

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Pradolini, G.G., Ramos, W.A. Characterization of Lipschitz Functions via the Commutators of Singular and Fractional Integral Operators in Variable Lebesgue Spaces. Potential Anal 46, 499–525 (2017). https://doi.org/10.1007/s11118-016-9592-8

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  • DOI: https://doi.org/10.1007/s11118-016-9592-8

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