Estimates for Fourier transforms of surface measures in \(\mathbb{R}^3\) and PDE applications

DOI10.4171/RMI/890zbMath1345.42006arXiv1302.4070OpenAlexW2964161982MaRDI QIDQ726763

Michael Greenblatt

Publication date: 14 July 2016

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4070

zbMATH Keywords

Fourier transformSchrödinger equationsheat equationsoscillatory integralsurface measures

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Harmonic analysis and PDEs (42B37)

Related Items (2)

Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces ⋮ Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms

Cites Work

• Unnamed Item
• Resolution of singularities in two dimensions and the stability of integrals
• Estimates for maximal functions associated with hypersurfaces in \(\mathbb R^3\) and related problems of harmonic analysis
• Uniform estimates for the Fourier transform of surface carried measures in \(\mathbb R^{3}\) and an application to Fourier restriction
• The asymptotic behavior of degenerate oscillatory integrals in two dimensions
• Uniform estimates of oscillatory integrals with parabolic or hyperbolic phase
• Hilbert transforms along curves. I: Nilpotent groups
• A theorem concerning uniform estimates of oscillatory integrals when the phase is a function of two variables
• Convex hypersurfaces and Fourier transforms
• The Newton polyhedron and oscillatory integral operators
• Decay of the Fourier transform of surfaces with vanishing curvature
• On adapted coordinate systems
• Uniform estimates for cubic oscillatory integrals
• Oscillatory Integrals and Fourier Transforms of Surface Carried Measures
• Oscillatory integrals, lagrange immersions and unfolding of singularities

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