Some sharp restriction inequalities

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• Diogo Oliveira e Silva (University of Bonn)
• Thursday 04 December 2014, 16:00-17:00
• Watson 310.

If you have a question about this talk, please contact José Cañizo.

The goal of this talk will be to find the sharp forms and characterize the complex-valued extremizers of the adjoint Fourier restriction inequalities on the sphere: ‖ℱ(f σ)‖_L^p(ℝ^d) ≲ ‖f‖_{L^q(S^d-1, σ)}, in the cases (d,p,q) = (d,2k, q) with d,k ∈ ℕ and q ∈ ℝ⁺ ∪ {∞} satisfying:

(a) k = 2, q ≥ 2 and 3 ≤ d ≤ 7;
(b) k = 2, q ≥ 4 and d ≥ 8;
(c) k ≥ 3, q ≥ 2k and d ≥ 2.

Tools include a spherical harmonic decomposition, the study of the Cauchy-Pexider functional equation for sumsets of the sphere, and a sharp multilinear weighted restriction inequality with weight related to the k-fold convolution of the surface measure. This topic builds up on recent results by D. Foschi, and is joint work with E. Carneiro.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• School of Mathematics events
• Watson 310

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