Authors: Isroil A Ikromov Detlef Müller
Publish Date: 2011/07/16
Volume: 17, Issue: 6, Pages: 1292-1332
Abstract
Let S be a hypersurface in BbbR3 which is the graph of a smooth finite type function φ and let μ=ρ dσ be a surface carried measure on S where dσ denotes the surface element on S and ρ a smooth density with sufficiently small support We derive uniform estimates for the Fourier transform hatmu of μ which are sharp except for the case where the principal face of the Newton polyhedron of φ when expressed in adapted coordinates is unbounded As an application we prove a sharp L p L 2 Fourier restriction theorem for S in the case where the original coordinates are adapted to φ This improves on earlier joint work with M Kempe
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