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The Journal of Geometric Analysis

, Volume 27, Issue 2, pp 1624–1635 | Cite as

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

  • María J. Carro
  • Carlos Domingo-Salazar
Article

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.

Keywords

Square functions Sparse operators Weighted inequalities 

Mathematics Subject Classification

42B25 42B37 

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Copyright information

© Mathematica Josephina, Inc. 2016

Authors and Affiliations

  1. 1.Departament de Matemàtiques i InformàticaUniversitat de BarcelonaBarcelonaSpain

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