Fourier restriction to polynomial curves I: a geometric inequality

@article{Dendrinos2010FourierRT,
  title={Fourier restriction to polynomial curves I: a geometric inequality},
  author={Spyridon Dendrinos and Spyridon James Wright},
  journal={American Journal of Mathematics},
  year={2010},
  volume={132},
  pages={1031 - 1076}
}
We prove a Fourier restriction result for general polynomial curves in ${\Bbb R}^d$. Measuring the Fourier restriction with respect to the affine arclength measure of the curve, we obtain a universal estimate for the class of all polynomial curves of bounded degree. Our method relies on establishing a geometric inequality for general polynomial curves which is of interest in its own right. Applications of this geometric inequality to other problems in euclidean harmonic analysis have recently… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 20 CITATIONS

Uniform estimates for Fourier restriction to polynomial curves in $\mathbb R^d$

VIEW 15 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Uniform estimates for Fourier restriction to polynomial curves in ℝd

VIEW 15 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Topics in affine and discrete harmonic analysis

VIEW 7 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Restriction estimates for space curves with respect to general measures

VIEW 11 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Restriction of Fourier transforms to some complex curves

VIEW 8 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-10 OF 21 REFERENCES

On the restriction of the Fourier transform to curves: endpoint results and degenerate cases

M. Christ
  • Trans. Amer. Math. Soc
  • 1985
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

On some rules of Laguerre’s and systems of equal sums of like powers, Rend

J. Steinig
  • 1971
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Shayya, Fourier restriction to convex surfaces in R3

F. Abi-Khuzam
  • Publ. Mat
  • 2006
VIEW 1 EXCERPT