On oscillatory integral operators with folding canonical relations

Allan Greenleaf; Andreas Seeger

Displaying similar documents to “On oscillatory integral operators with folding canonical relations”

Oscillatory and Fourier integral operators with degenerate canonical relations.

Allan Greenleaf, Andreas Seeger (2002)

Publicacions Matemàtiques

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We survey results concerning the L² boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

$L^{2}$ Estimates for Oscillatory Integrals

G. Sampson (1998)

Colloquium Mathematicae

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Oscillatory integrals and multiplier problem for the disc

Lennart Carleson, Per Sjölin (1972)

Studia Mathematica

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$L^{2}$ 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.

$L^{p}$ and Hölder estimates for pseudodifferential operators : sufficient conditions

Richard Beals (1979)

Annales de l'institut Fourier

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Continuity in $L^{p}$ spaces and spaces of Hölder type is proved for pseudodifferential operators of order zero, under general conditions on the class of symbols. Applications to the regularity theory of some hypoelliptic operators are outlined.

Ψ-pseudodifferential operators and estimates for maximal oscillatory integrals

Carlos E. Kenig, Wolfgang Staubach (2007)

Studia Mathematica

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We define a class of pseudodifferential operators with symbols a(x,ξ) without any regularity assumptions in the x variable and explore their $L^{p}$ boundedness properties. The results are applied to obtain estimates for certain maximal operators associated with oscillatory singular integrals.

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

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A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators....

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.

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.

Uniform boundedness of oscillatory singular integrals on Hardy spaces.

Leslie C. Cheng, Yibiao Pan (2000)

Publicacions Matemàtiques

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We prove the uniform H boundedness of oscillatory singular integrals with degenerate phase functions.