## On Fourier restriction and the Newton polygon

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**137**(2009), 615-625 Request permission

## Abstract:

Local $L^p\to L^2$ bounds are proved for the restriction of the Fourier transform to analytic surfaces of the form $S=(x,f(x))$ in $\mathbb {R}^3$. It is found that the range of exponents is determined by the so-called distance of the Newton polygon, associated to $f$, except when the principal quasi-homogeneous part of $f(x)$ contains a factor of high multiplicity. The proofs are based on the method of Phong-Stein and Rychkov, adapted to scalar oscillatory integrals.## References

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## Additional Information

**Ákos Magyar**- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- Address at time of publication: Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Room 121, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 318009
- Email: amagyar2000@yahoo.com
- Received by editor(s): August 20, 2007
- Received by editor(s) in revised form: January 25, 2008
- Published electronically: August 26, 2008
- Additional Notes: This research was supported in part by NSF Grant DMS-0456490
- Communicated by: Andreas Seeger
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**137**(2009), 615-625 - MSC (2000): Primary 42B10; Secondary 43A32
- DOI: https://doi.org/10.1090/S0002-9939-08-09510-5
- MathSciNet review: 2448583