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$ L^p$-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves


Author: Neal Bez
Journal: Proc. Amer. Math. Soc. 135 (2007), 151-161
MSC (2000): Primary 42B15
DOI: https://doi.org/10.1090/S0002-9939-06-08603-5
Published electronically: June 20, 2006
MathSciNet review: 2280201
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Abstract: Some sufficient conditions on a real polynomial $ P$ and a convex function $ \gamma$ are given in order for the Hilbert transform and maximal operator along $ (t,P(\gamma(t)))$ to be bounded on $ L^p$, for all $ p$ in $ (1,\infty)$, with bounds independent of the coefficients of $ P$. The same conclusion is shown to hold for the corresponding hypersurface in $ \mathbb{R}^{d+1}$ $ (d \geq 2)$ under weaker hypotheses on $ \gamma$.


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Additional Information

Neal Bez
Affiliation: School of Mathematics, University of Edinburgh, Kings’s Buildings, Edinburgh, EH3 9JZ United Kingdom
Email: n.r.bez@sms.ed.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-06-08603-5
Received by editor(s): July 26, 2005
Published electronically: June 20, 2006
Additional Notes: The author was supported by an EPSRC award
Communicated by: Michael Lacey
Article copyright: © Copyright 2006 American Mathematical Society

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