On the Haar shift representations of Calderón-Zygmund operators
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- by Tuomas Orponen PDF
- Proc. Amer. Math. Soc. 141 (2013), 2693-2698 Request permission
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
- Tuomas P. Hytönen, The sharp weighted bound for general Calderón-Zygmund operators, Ann. of Math. (2) 175 (2012), no. 3, 1473–1506. MR 2912709, DOI 10.4007/annals.2012.175.3.9
- 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
- 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
Additional Information
- Tuomas Orponen
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, FI-00014 Helsinki, Finland
- MR Author ID: 953075
- Email: tuomas.orponen@helsinki.fi
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2693-2698
- MSC (2010): Primary 42B20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11624-2
- MathSciNet review: 3056559