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Recovering singular integrals from Haar shifts


Author: Armen Vagharshakyan
Journal: Proc. Amer. Math. Soc. 138 (2010), 4303-4309
MSC (2010): Primary 42B20, 42A45
DOI: https://doi.org/10.1090/S0002-9939-2010-10426-4
Published electronically: June 15, 2010
MathSciNet review: 2680056
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Abstract: We recover one-dimensional Calderón-Zygmund convolution operators with sufficiently smooth kernels by means of a properly chosen averaging of certain dyadic shift operators. As a corollary, a sharp $ A_2$ inequality for these Calderón-Zygmund operators is derived from a corresponding inequality for dyadic shift operators.


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Additional Information

Armen Vagharshakyan
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: armenv@math.gatech.edu, armen@math.brown.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10426-4
Received by editor(s): January 28, 2010
Published electronically: June 15, 2010
Additional Notes: This research was supported in part by NSF grant 0456611
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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