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Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Haar shift representations of Calderón-Zygmund operators


Author: Tuomas Orponen
Journal: Proc. Amer. Math. Soc. 141 (2013), 2693-2698
MSC (2010): Primary 42B20
Published electronically: April 3, 2013
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Abstract: In connection with proving the $ A_{2}$ conjecture in 2010, T. Hytönen obtained a representation of general Calderón-Zygmund operators in terms of simpler operators known as Haar shifts. In this note, we prove that the result is sharp in the sense that Haar shift representations of Hytönen's type are only available for Calderón-Zygmund operators.


References [Enhancements On Off] (What's this?)

  • [1] Tuomas P. Hytönen, The sharp weighted bound for general Calderón-Zygmund operators, Ann. of Math. (2) 175 (2012), no. 3, 1473–1506. MR 2912709, http://dx.doi.org/10.4007/annals.2012.175.3.9
  • [2] T. Hytönen, M. Lacey, H. Martikainen, T. Orponen, M. Reguera, E. Sawyer, and I. Uriarte-Tuero: Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators, to appear in J. Anal. Math., available at arXiv:1103.5229
  • [3] T. Hytönen, C. Pérez, S. Treil, and A. Volberg: Sharp weighted estimates for dyadic shifts and the $ A_{2}$ conjecture, to appear in J. Reine Angew. Math. (2012), available at arXiv:1010.0755

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Additional Information

Tuomas Orponen
Affiliation: Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, FI-00014 Helsinki, Finland
Email: tuomas.orponen@helsinki.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11624-2
PII: S 0002-9939(2013)11624-2
Received by editor(s): October 24, 2011
Published electronically: April 3, 2013
Additional Notes: The author was supported by the Finnish Centre of Excellence in Analysis and Dynamics Research
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.