$L^p$-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves
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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 $\gamma$.References
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Additional Information
- Neal Bez
- Affiliation: School of Mathematics, University of Edinburgh, Kings’s Buildings, Edinburgh, EH3 9JZ United Kingdom
- MR Author ID: 803270
- Email: n.r.bez@sms.ed.ac.uk
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 151-161
- MSC (2000): Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9939-06-08603-5
- MathSciNet review: 2280201