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Local Fractional and singular integrals on open subsets

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Abstract

For a proper open set Ω immersed in a metric space with the weak homogeneity property, and given a measure μ doubling on a certain family of balls lying “well inside” of Ω, we introduce local operators of singular and fractional type and study their boundedness properties on weighted Lp(Ω), 1 ≤ p < ∞, for weights in local Muckenhoupt classes.

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Authors and Affiliations

  1. Instituto de Matemática Aplicada del Litoral CONICET-UNL, and Facultad de Ingeniería Química, UNL, Colectora Ruta Nac N°168, Paraje El Pozo, 3000, Santa Fe, Argentina

    Eleonor Harboure, Oscar Salinas & Beatriz Viviani

Authors
  1. Eleonor Harboure
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  2. Oscar Salinas
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  3. Beatriz Viviani
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Corresponding author

Correspondence to Oscar Salinas.

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Harboure, E., Salinas, O. & Viviani, B. Local Fractional and singular integrals on open subsets. JAMA 138, 301–324 (2019). https://doi.org/10.1007/s11854-019-0034-6

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  • DOI: https://doi.org/10.1007/s11854-019-0034-6

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