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Commutators of Singular Integrals with Kernels Satisfying Generalized Hörmander Conditions and Extrapolation Results to the Variable Exponent Spaces

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Abstract

We obtain boundedness results for the higher order commutators of singular integral operators between weighted Lebesgue spaces, including Lp-BMO and Lp-Lipschitz estimates. The kernels of such operators satisfy certain regularity condition, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of singular integral operators with less regular kernels satisfying a Hörmander’s type inequality. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p. Finally, by extrapolation techniques, we derive different results in the variable exponent context.

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Authors and Affiliations

  1. Facultad de Ingeniería Química, CONICET-UNL, Santa Fe, Argentina

    Luciana Melchiori & Gladis Pradolini

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  1. Luciana Melchiori
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  2. Gladis Pradolini
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Correspondence to Luciana Melchiori.

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Melchiori, L., Pradolini, G. Commutators of Singular Integrals with Kernels Satisfying Generalized Hörmander Conditions and Extrapolation Results to the Variable Exponent Spaces. Potential Anal 51, 579–601 (2019). https://doi.org/10.1007/s11118-018-9726-2

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