Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction
By Isroil A. Ikromov, D. Müller. 2010
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AbstractLet S be a hypersurface in ${\Bbb{R}}^{3}$ 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 $\hat{\mu}$ 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 Lp-L2 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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c6af7a5e1a5c4248ae772ea14119d9db491238f0
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In Applied Mathematics
- M. Pramanik
- Tristan C. Collins
- Allan Greenleaf
- D. Müller
- Isroil A. Ikromov
- Dachun Yang
- Chi Li
- Yuan Zhou
In Geometry and Topology
Citations in the corpus
- A multi-dimensional resolution of singularities with applications to analysis (2010, methodology): “Acknowledgements The third author thanks Professor Detlef Müller for valuable comments and Professor Kalle Karu for mentioning a reference for Lemma 2.4.”
- Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (2016, methodology): “Ikromov and Müller [15] proved extensions of this inequality to the smooth category.”