On sharp Strichartz inequalities in low dimensions

By Dirk Hundertmark, Vadim Zharnitsky. 2006

119 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/96c1f3429ad925f14c04c7b6a934a73dcce4fcaa

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The geodesic X-ray transform with fold caustics (2010, background): “It is known [Foschi 2007; Hundertmark and Zharnitsky 2006] that any Gaussian is an extremizer for the paraboloid, and conversely.”
A Sharp Inequality for the Strichartz Norm (2008, background): “Later, Foschi [4] and Hundertmark-Zharnitsky [6] independently obtained the sharp constants in the cases n = 1, (q, r) = (6, 6); and n = 2, (q, r) = (4, 4); showing that the only maximizers are Gaussians.”
Maximizers for the Stein–Tomas Inequality (2016, unknown): “We cite the following conjecture from [14]; see also [21].”
Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation (2009, methodology): “Kunze [13] treated the d = 1 case and showed that maximizers exist by an elaborate concentration-compactness method; when d = 1, 2, Foschi [7] explicitly determined the best constants and showed that the only maximizers are Gaussians by using the sharp Cauchy-Schwarz inequality and the space-time Fo”
The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality (2008, result): “Recently, Carneiro [2008] proved a sharp Strichartz-type inequality by following the arguments in [Hundertmark and Zharnitsky 2006] and found its maximizers, which derives the same results in [Hundertmark and Zharnitsky 2006] as a corollary when d = 1, 2.”
Maximizers for the Strichartz Inequalities for the wave equation (2009, methodology): “[10] D. Hundertmark and V. Zharnitsky, On sharp Strichartz inequalities in low dimensions, Int.”
Existence of Extremals for a Fourier Restriction Inequality (2010, background): “It is known [Foschi 2007; Hundertmark and Zharnitsky 2006] that any Gaussian is an extremizer for the paraboloid, and conversely.”
Heat-flow monotonicity of Strichartz norms (2008, methodology): “2, combined with a further argument from [Hundertmark and Zharnitsky 2006] (where explicit details can be found), shows that Gaussians are the only extremisers of the Strichartz inequality in the cases (d, p, q)= (1, 6, 6), (2, 4, 4).”