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

Yibiao Pan; Gary Sampson; Paweł Szeptycki

Displaying similar documents to “ $L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains”

$L^{2}$ 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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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.

An oscillatory singular integral operator with polynomial phase

Josfina Alvarez, Jorge Hounie (1999)

Studia Mathematica

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We prove the continuity of an oscillatory singular integral operator T with polynomial phase P(x,y) on an atomic space $H_{P}^{1}$ related to the phase P. Moreover, we show that the cancellation condition to be imposed on T holds under more general conditions. To that purpose, we obtain a van der Corput type lemma with integrability at infinity.

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].

Weighted weak type (1,1) estimates for oscillatory singular integrals

Shuichi Sato (2000)

Studia Mathematica

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We consider the $A_{1}$ -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.

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

Anthony Carbery, James Wright (2002)

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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 involving a derivative of fractional order

Margaret Murray (1987)

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Singular integrals on product H spaces.

Robert Fefferman (1985)

Revista Matemática Iberoamericana

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Kernel estimates for fractional integrals with polynomial weights

Jan-Olov Strömberg, Richard Wheeden (1986)

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Oscillatory singular integrals on weighted Hardy spaces

Yue Hu (1992)

Studia Mathematica

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Let $T f (x) = p . v . ʃ_{ℝ ¹} e^{i P (x - y)} f (y) / (x - y) d y$ , where P is a real polynomial on ℝ. It is proved that T is bounded on the weighted H¹(wdx) space with w ∈ A₁.

Displaying similar documents to “ L 2 and L p estimates for oscillatory integrals and their extended domains”

Displaying similar documents to “ $L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains”