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Mixed Inequalities for Operators Associated to Critical Radius Functions with Applications to Schrödinger Type Operators

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Abstract

We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schrödinger Calderón-Zygmund operators of (s,δ) type, for \(1<s\leq \infty \) and 0 < δ ≤ 1. We also give estimates of the same type for the associated maximal operators. As an application, we obtain a wide variety of mixed inequalities for Schrödinger type singular integrals. As far as we know, these results are a first approach of mixed inequalities in the Schrödinger setting.

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Funding

The authors were supported by PICT 2019 No 389 (ANPCyT) and CAI+D 2019 50320220100210 (UNL)

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Authors and Affiliations

  1. CONICET, Santa Fe, Argentina

    Fabio Berra & Gladis Pradolini

  2. Departamento de Matemática (FIQ-UNL), Santa Fe, Argentina

    Fabio Berra & Gladis Pradolini

  3. Instituto de Matemática Aplicada del Litoral (IMAL) (UNL, CONICET), Colectora Ruta Nac. N 168, Paraje El Pozo. 3000, Santa Fe, Argentina

    Pablo Quijano

Authors
  1. Fabio Berra
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  2. Gladis Pradolini
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  3. Pablo Quijano
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Correspondence to Fabio Berra.

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Berra, F., Pradolini, G. & Quijano, P. Mixed Inequalities for Operators Associated to Critical Radius Functions with Applications to Schrödinger Type Operators. Potential Anal 60, 253–283 (2024). https://doi.org/10.1007/s11118-022-10049-2

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  • DOI: https://doi.org/10.1007/s11118-022-10049-2

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