Year: 2020
Type: article
Abstract: In their work Ikromov and Müller (Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra. Princeton University Press, Princeton, 2016) proved the full range $$L^p-L^2$$ L p - L 2 Fourier restriction estimates for a very general class of hypersurfaces in $${\mathbb {R}}^3$$ R 3 which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed norm case where the coordinates are split in two directions, one tangential and the other normal to the surface at a fixed given point. In particular, we resolve completely the adapted case and partly the non-adapted case. In the non-adapted case the case when the linear height $$h_\text {lin}(\phi )$$ h lin ( ϕ ) is below two is settled completely.
Source: Mathematische Zeitschrift
Author: Ljudevit Palle
Institution: Christian-Albrechts-Universität zu Kiel
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,750
OpenAlex ID: W3040943020