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Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces

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Abstract

Let μ be a nonnegative Borel measure on Rd satisfying that μ(Q) ⩽ l(Q)n for every cube Q ⊂ Rn, where l(Q) is the side length of the cube Q and 0 < n ⩽ d.

We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function B in the context of non-homogeneous spaces related to the measure μ. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W.Wang, C. Tan, Z. Lou (2012).

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Authors and Affiliations

  1. Facultad de Ingeniería Química (CONICET UNL), Santiago del Estero 2829, 3000, Santa Fe, Argentina

    Gladis Pradolini

  2. Instituto de Matemática Bahía Blanca (CONICET UNS), and Departamento de Matemáticas (UNS), Av. Alem 1253, Bahía Blanca, 8000, Argentina

    Jorgelina Recchi

Authors
  1. Gladis Pradolini
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  2. Jorgelina Recchi
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Correspondence to Gladis Pradolini.

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Pradolini, G., Recchi, J. Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces. Czech Math J 68, 77–94 (2018). https://doi.org/10.21136/CMJ.2018.0337-16

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  • DOI: https://doi.org/10.21136/CMJ.2018.0337-16

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