Uniform estimates for Fourier restriction to polynomial curves in ℝ d

Stovall, Betsy

doi:10.1353/ajm.2016.0021

Cited by 16 publications

(29 citation statements)

References 59 publications

(105 reference statements)

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“…On the other hand, when the dimension of the manifold is one, namely, when the associated surface is a curve, the restriction estimate is by now fairly well understood [4][5][6]26].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Bilinear restriction estimates for surfaces of codimension bigger than 1

Bak

Lee

2017

Analysis & PDE

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Abstract. In connection with the restriction problem in R n for hypersurfaces including the sphere and paraboloid, the bilinear (adjoint) restriction estimates have been extensively studied. However, not much is known about such estimates for surfaces with codimension (and dimension) larger than one. In this paper we show sharp bilinear L 2 × L 2 → L q restriction estimates for general surfaces of higher codimension. In some special cases, we can apply these results to obtain the corresponding linear estimates.

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“…On the other hand, when the dimension of the manifold is one, namely, when the associated surface is a curve, the restriction estimate is by now fairly well understood [4][5][6]26].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Bilinear restriction estimates for surfaces of codimension bigger than 1

Bak

Lee

2017

Analysis & PDE

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“…This is known if d = 2 [22]. In fact, a uniform restriction result is known for polynomial curves with affine arclength measure in all dimensions ( [24] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Linear and bilinear restriction to certain rotationally symmetric hypersurfaces

Stovall

2016

Trans. Amer. Math. Soc.

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Abstract. Conditional on Fourier restriction estimates for elliptic hypersurfaces, we prove optimal restriction estimates for polynomial hypersurfaces of revolution for which the defining polynomial has non-negative coefficients. In particular, we obtain uniform-depending only on the dimension and polynomial degree-estimates for restriction with affine surface measure, slightly beyond the bilinear range. The main step in the proof of our linear result is an (unconditional) bilinear adjoint restriction estimate for pieces at different scales.

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“…2 +ω) 1 q = 1 was shown in [29,Section 5]. If ω = d − 1, the range of p, q in Proposition 1.5 becomes the smallest but it properly contains the range p, q in Theorem 1.1.…”

Section: Introductionmentioning

confidence: 90%

“…The projection of a nondegenerate polynomial curve in R d to (d−1)-dimensional hyperplane can be seen as a degenerate polynomial curve in R d−1 . So, Proposition 1.5 also can be deduced from the Fourier restriction theorem for polynomial curves with affine arclength measure (see [27,28,12,16,17,3,29]).…”

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confidence: 96%