Fourier restriction above rectangles

• DOI: 10.48550/arxiv.1911.11600
• Publication Date: 2019-01-01
• Authors: Jeremy Schwend; Betsy Stovall
• Keywords: Operator (biology)

In this article, we study the problem of obtaining Lebesgue space inequalities for Fourier restriction operator associated to rectangular pieces paraboloid and perturbations thereof. We state a conjecture dependence norms in these on sidelengths rectangles, prove that follows from (a slight reformulation the) elliptic hypersurfaces, that, if valid, is essentially sharp. Such questions arise naturally degenerate hypersurfaces; demonstrate connection by using our positive results new class hypersurfaces having some additive structure.