Oscillatory integrals with polynomial phases

DOI10.1007/BF01231323zbMath0829.42014OpenAlexW1978921923MaRDI QIDQ1209124

Duong H. Phong

Publication date: 16 May 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144041

zbMATH Keywords

homogeneous polynomialoscillatory integrals\(L^ 2\)-bounds

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fourier integral operators applied to PDEs (35S30) Pseudodifferential operators (47G30)

Related Items (22)

The mapping properties for a class of oscillatory integrals ⋮ On the Fourier transform of measures carried by submanifolds of finite type ⋮ \(L^2\) estimates for averaging operators along curves with two-sided \(k\)-fold singularities ⋮ Sharp \(L^{p}\)-boundedness of oscillatory integral operators with polynomial phases ⋮ Oscillatory integral operators with homogeneous polynomial phases in several variables ⋮ The Newton polyhedron and oscillatory integral operators ⋮ Sharp \(L^p\) decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables ⋮ Some new decay estimates for \((2+1)\)-dimensional degenerate oscillatory integral operators ⋮ A sharp decay estimate for degenerate oscillatory integral operators using broad-narrow method ⋮ Sharp \(L^p\) decay estimates for degenerate and singular oscillatory integral operators: homogeneous polynomial phases ⋮ An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems ⋮ Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases ⋮ New convolutions for quadratic-phase Fourier integral operators and their applications ⋮ A few endpoint geodesic restriction estimates for eigenfunctions ⋮ \(L^p\) decay estimates for weighted oscillatory integral operators on \(\mathbb R\) ⋮ On Fourier restriction and the Newton polygon ⋮ Van der Corput lemmas for Mittag-Leffler functions. II: \(\alpha\)-directions ⋮ Decay rates of oscillatory integral operators in “1 + 2” dimensions ⋮ The complete \((L^p,L^p)\) mapping properties for a class of oscillatory integrals ⋮ A survey on oscillatory integral operators ⋮ Estimates on level set integral operators in dimension two ⋮ Degenerate Fourier integral operators in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Composition of some singular Fourier integral operators and estimates for restricted X-ray transforms
• Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle
• Equivalence of glancing hyper-surfaces
• Fourier integral operators. I
• Propagation, reflection, and diffraction of singularities of solutions to wave equations
• Problems in harmonic analysis related to curvature
• Cosmology in (2 + 1) -Dimensions, Cyclic Models, and Deformations of M2,1. (AM-121)
• Oscillatory integrals associated to folding canonical relations

This page was built for publication: Oscillatory integrals with polynomial phases