A restriction estimate using polynomial partitioning

Guth, Larry¹

¹ Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139

Journal of the American Mathematical Society, Tome 29 (2016) no. 2, pp. 371-413

Résumé

If $S$ is a smooth compact surface in $\mathbb {R}^3$ with strictly positive second fundamental form, and $E_S$ is the corresponding extension operator, then we prove that for all $p > 3.25$, $\| E_S f\|_{L^p(\mathbb {R}^3)} \le C(p,S) \| f \|_{L^\infty (S)}$. The proof uses polynomial partitioning arguments from incidence geometry.

Détail

DOI : 10.1090/jams827

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