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A sparse approach to mixed weak type inequalities

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Abstract

In this paper we provide some quantitative mixed weak-type estimates assuming conditions that imply that \(uv\in A_{\infty }\) for Calderón–Zygmund operators, rough singular integrals and commutators. The main novelty of this paper lies in the fact that we rely upon sparse domination results, pushing an approach to endpoint estimates that was introduced in Domingo-Salazar et al. (Bull Lond Math Soc 48(1):63–73, 2016) and extended in Lerner et al. (Adv Math 319:153–181, 2017) and Li et al. (J Geom Anal, 2018).

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Acknowledgements

The authors would like to thank Sheldy Ombrosi for his comments on an earlier version of this manuscript and for some enlightening discussions on this topic.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Nacional del Sur, Alem 1253, Bahía Blanca, Argentina

    Marcela Caldarelli & Israel P. Rivera-Ríos

  2. INMABB, CONICET, Alem 1253, Bahía Blanca, Argentina

    Israel P. Rivera-Ríos

Authors
  1. Marcela Caldarelli
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  2. Israel P. Rivera-Ríos
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Correspondence to Israel P. Rivera-Ríos.

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I. P. Rivera-Ríos is supported by CONICET PIP 11220130100329CO.

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Caldarelli, M., Rivera-Ríos, I.P. A sparse approach to mixed weak type inequalities. Math. Z. 296, 787–812 (2020). https://doi.org/10.1007/s00209-019-02447-x

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