Oscillatory and Fourier integral operators with degenerate canonical relations.

Allan Greenleaf; Andreas Seeger

Displaying similar documents to “Oscillatory and Fourier integral operators with degenerate canonical relations.”

On oscillatory integral operators with folding canonical relations

Allan Greenleaf, Andreas Seeger (1999)

Studia Mathematica

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Sharp $L^{p}$ estimates are proven for oscillatory integrals with phase functions Φ(x,y), (x,y) ∈ X × Y, under the assumption that the canonical relation $C_{Φ}$ projects to T*X and T*Y with fold singularities.

$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

Yibiao Pan, Gary Sampson, Paweł Szeptycki (1997)

Studia Mathematica

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We prove the $L^{p}$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function ${| x |}^{α} {| y |}^{β}$ . Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.

Estimates of one-dimensional oscillatory integrals

Detlef Muller (1983)

Annales de l'institut Fourier

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We study one-dimensional oscillator integrals which arise as Fourier-Stieltjes transforms of smooth, compactly supported measures on smooth curves in Euclidean spaces and determine their decay at infinity, provided the curves satisfy certain geometric conditions.

$L^{2}$ Estimates for Oscillatory Integrals

G. Sampson (1998)

Colloquium Mathematicae

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Composition of some singular Fourier integral operators and estimates for restricted $X$ -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

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We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations $C \subset (T^{*} X ∖ 0) \times (T^{*} Y ∖ 0)$ . These canonical relations, which arise naturally in integral geometry, are such that $π$ : $C \to T^{*} Y$ is a Whitney fold and $ρ$ : $C \to T^{*} X$ is a blow-down mapping. If $A \in I^{m} (C)$ , $B \in I^{m^{'}} (C^{t})$ , then $B A \in I^{m + m^{'}, 0} (Δ, Λ)$ a class of pseudodifferential operators with singular symbols. From this follows $L^{2}$ boundedness of $A$ with a loss of 1/4 derivative.

Oscillatory integrals and multiplier problem for the disc

Lennart Carleson, Per Sjölin (1972)

Studia Mathematica

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A Calderón-Zygmund estimate with applications to generalized Radon transforms and Fourier integral operators

Malabika Pramanik, Keith M. Rogers, Andreas Seeger (2011)

Studia Mathematica

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We prove a Calderón-Zygmund type estimate which can be applied to sharpen known regularity results on spherical means, Fourier integral operators, generalized Radon transforms and singular oscillatory integrals.

What is van der Corput's lemma in higher dimensions?

Anthony Carbery, James Wright (2002)

Publicacions Matemàtiques

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We consider variants of van der Corput's lemma in higher dimensions. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Multilinear singular integrals.

Christoph M. Thiele (2002)

Publicacions Matemàtiques

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We survey the theory of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators. ...