Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An affine restriction estimate in $ \mathbb{R}^3$


Author: Bassam Shayya
Journal: Proc. Amer. Math. Soc. 135 (2007), 1107-1113
MSC (2000): Primary 42B10; Secondary 52A15.
DOI: https://doi.org/10.1090/S0002-9939-06-08604-7
Published electronically: September 26, 2006
MathSciNet review: 2262912
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the Fourier transform of an $ L^{4/3}$ function can be restricted to any compact convex $ C^2$ surface of revolution in $ \mathbb{R}^3$.


References [Enhancements On Off] (What's this?)

  • 1. F. ABI-KHUZAM AND B. SHAYYA, Fourier restriction to convex surfaces of revolution in $ \mathbb{R}^3$, Publ. Mat. 50 (2006), 71-85.
  • 2. A. D. ALEKSANDROV, Almost everywhere existence of the second differential of a convex function and some properties of convex surfaces connected with it (in Russian), Uch. Zap. Leningrad. Gos. Univ., Math. Ser. 6 (1939), 3-35. MR 0003051 (2:155a)
  • 3. A. CARBERY AND S. ZIESLER, Restriction and decay for flat hypersurfaces, Publ. Mat. 46 (2002), 405-434. MR 1934361 (2003i:42019)
  • 4. G. DOLZMANN AND D. HUG, Equality of two representations of extended affine surface area, Arch. Math. 65 (1995), 352-356. MR 1349190 (97c:52019)
  • 5. D. HUG, Contributions to affine surface area, Manuscripta Math. 91 (1996), 283-301. MR 1416712 (98d:52009)
  • 6. M. LUDWIG AND M. REITZNER, A characterization of affine surface area, Adv. Math. 147 (1999), 138-172. MR 1725817 (2000j:52018)
  • 7. E. LUTWAK, Extended affine surface area, Adv. Math. 85 (1991), 39-68. MR 1087796 (92d:52012)
  • 8. D. OBERLIN, Fourier restriction for affine arclength measures in the plane, Proc. Amer. Math. Soc. 129 (2001), 3303-3305. MR 1845006 (2002g:42013)
  • 9. D. OBERLIN, A uniform Fourier restriction theorem for surfaces in $ \mathbb{R}^3$, Proc. Amer. Math. Soc. 132 (2004), 1195-1199. MR 2045437 (2005h:42020)
  • 10. D. OBERLIN, Two estimates for curves in the plane, Proc. Amer. Math. Soc. 132 (2004), 3195-3201. MR 2073293 (2005f:42037)
  • 11. C. SCH¨UTT, On the affine surface area, Proc. Amer. Math. Soc. 118 (1993), 1213-1218. MR 1181173 (93j:52009)
  • 12. C. SCH¨UTT AND E. WERNER, The convex floating body, Math. Scand. 66 (1990), 275-290. MR 1075144 (91i:52005)
  • 13. P. SJÖLIN, Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in $ \mathbb{R}^2$, Studia Math. 51 (1974), 169-182. MR 0385437 (52:6299)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B10, 52A15.

Retrieve articles in all journals with MSC (2000): 42B10, 52A15.


Additional Information

Bassam Shayya
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: bshayya@aub.edu.lb

DOI: https://doi.org/10.1090/S0002-9939-06-08604-7
Received by editor(s): November 7, 2005
Published electronically: September 26, 2006
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society