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

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].

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].

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.