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Sharp \(A_{1}\) Weighted Estimates for Vector-Valued Operators

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Abstract

Given \(1\le q<p<\infty \), quantitative weighted \(L^{p}\) estimates, in terms of \(A_{q}\) weights, for vector-valued maximal functions, Calderón–Zygmund operators, commutators, and maximal rough singular integrals are obtained. The results for singular operators will rely upon suitable convex body domination results, which in the case of commutators will be provided in this work, obtaining as a byproduct a new proof for the scalar case as well.

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Acknowledgements

We would like to thank Francesco Di Plinio for suggesting us to address the problem of the maximal rough singular integral. The third author would like to express his gratitude to the Department of Mathematics of Lund University for the hospitality shown during his visit between September and November 2017.

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Authors and Affiliations

  1. Department of Mathematics, University at Albany, 1400 Washington Ave., Albany, NY, 12159, USA

    Joshua Isralowitz

  2. Centre for Mathematical Sciences, University of Lund, Lund, Sweden

    Sandra Pott

  3. Instituto de Matemática (INMABB), Departamento de Matemática, Universidad Nacional del Sur (UNS)-CONICET, Bahía Blanca, Argentina

    Israel P. Rivera-Ríos

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  1. Joshua Isralowitz
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  2. Sandra Pott
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  3. Israel P. Rivera-Ríos
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Correspondence to Israel P. Rivera-Ríos.

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Isralowitz, J., Pott, S. & Rivera-Ríos, I.P. Sharp \(A_{1}\) Weighted Estimates for Vector-Valued Operators. J Geom Anal 31, 3085–3116 (2021). https://doi.org/10.1007/s12220-020-00385-3

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