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Uniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 138, Number 4, August 2016
- pp. 907-962
- 10.1353/ajm.2016.0030
- Article
- Additional Information
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We study the bilinear Hilbert transforms and bilinear maximal functions associated to non-flat polynomial curves and obtain uniform $L^r$ estimates for $r>{d-1\over d}$, where $d$ is the degree of the polynomial. In addition, the lower bound of $r$ is sharp up to the end point.