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Mathematische Annalen

, Volume 365, Issue 3–4, pp 1111–1135 | Cite as

A pointwise estimate for positive dyadic shifts and some applications

  • José M. Conde-Alonso
  • Guillermo ReyEmail author
Article

Abstract

We prove a (sharp) pointwise estimate for positive dyadic shifts of complexity m which is linear in the complexity. This can be used to give a pointwise estimate for Calderón-Zygmund operators and to answer a question originally posed by Lerner. Several applications to weighted estimates for both multilinear Calderón-Zygmund operators and square functions are discussed.

Notes

Acknowledgments

The authors wish to thank Javier Parcet, Ignacio Uriarte-Tuero and Alexander Volberg for insightful discussions, and Andrei Lerner and Fedor Nazarov for sharing with us the details of their construction.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCMMadridSpain
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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