Recovering singular integrals from Haar shifts
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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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2680056