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The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces

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Abstract

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including L2-Lq, Lq-BMO and L2-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.

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Authors and Affiliations

  1. Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQ Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe, Colectora Ruta Nacional No 168, Santa Fe, Argentina

    Dalmasso Estefanía

  2. Facultad de Ingeniería Química, UNL, Santa Fe, Argentina

    Gladis Pradolini

  3. Facultad de Ciencias Exactas y Naturales y Agrimensura, UNNE, Corrientes, Argentina

    Wilfredo Ramos

Authors
  1. Dalmasso Estefanía
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  2. Gladis Pradolini
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  3. Wilfredo Ramos
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Correspondence to Dalmasso Estefanía.

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Estefanía, D., Pradolini, G. & Ramos, W. The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces. FCAA 21, 628–653 (2018). https://doi.org/10.1515/fca-2018-0034

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