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Stein’s Square Function \(G_\alpha \) and Sparse Operators

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Abstract

The purpose of this paper is to check that the square function \(G_\alpha \), introduced by E.M. Stein in 1958, can be controlled by a finite sum of sparse operators when \(\alpha >\frac{n+1}{2}\). This provides a useful tool to obtain weighted estimates for \(G_\alpha \) and related Fourier multipliers.

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Authors and Affiliations

  1. Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007, Barcelona, Spain

    María J. Carro & Carlos Domingo-Salazar

Authors
  1. María J. Carro
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  2. Carlos Domingo-Salazar
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Correspondence to María J. Carro.

Additional information

The authors were supported by Grants MTM2013-40985-P and 2014SGR289.

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Carro, M.J., Domingo-Salazar, C. Stein’s Square Function \(G_\alpha \) and Sparse Operators. J Geom Anal 27, 1624–1635 (2017). https://doi.org/10.1007/s12220-016-9733-8

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  • DOI: https://doi.org/10.1007/s12220-016-9733-8

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