2021
DOI: 10.1007/978-3-030-72058-2_7
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Young’s Inequality Sharpened

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Cited by 4 publications
(5 citation statements)
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“…The core of Theorem 1 is contained in the following proposition which treats the case where ρ differs from a ball only in a shell around the surface of this ball with relative width of order A[ρ] and where ρ is, in a certain sense, centered at the center of this ball. This corresponds to the arguments in [6,Sections 6,7,10].…”
Section: Proof Of the Bound For Small Perturbationsmentioning
confidence: 70%
See 2 more Smart Citations
“…The core of Theorem 1 is contained in the following proposition which treats the case where ρ differs from a ball only in a shell around the surface of this ball with relative width of order A[ρ] and where ρ is, in a certain sense, centered at the center of this ball. This corresponds to the arguments in [6,Sections 6,7,10].…”
Section: Proof Of the Bound For Small Perturbationsmentioning
confidence: 70%
“…Another complication comes from additional zero modes due to an additional symmetry. Similar difficulties were overcome in Christ's proof of a quantitative stability theorem for Young's convolution inequality [7]. The Hessian there is treated explicitly in terms of Hermite functions, whose role is similar to that of spherical harmonics here.…”
Section: Explicit Spectral Analysismentioning
confidence: 90%
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“…Fifteen years later, Lieb [95] went farther, proving that all maximizers are in fact gaussians. Much more recently, in 2014, Christ [45] obtained a stabler form of uniqueness of maximizers, and a sharper inequality: If 1 < p < 2 and d ≥ 1, then there exists c = c(p, d) > 0 such that, for any nonzero f ∈ L p ,…”
Section: Introductionmentioning
confidence: 99%
“…Here G denotes the set of gaussians G(x) = a exp(−Q(x)+x•v), with (a, v) ∈ C×C d and Q a positive definite real quadratic form. Christ's analysis [45] proceeds by contradiction, and its key step is a non-quantitative concentration-compactness result which relies on inverse theorems of Balog-Szemerédi and Freȋman from additive combinatorics. Consequently, the stability constant c in ( 6) is not obtained in explicit form, nor is it quantified in any way.…”
Section: Introductionmentioning
confidence: 99%