Displaying similar documents to “ L 2 Estimates for Oscillatory Integrals”

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.

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 estimation for a family of oscillatory integrals

Magali Folch-Gabayet, James Wright (2003)

Studia Mathematica

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Let K be a Calderón-Zygmund kernel and P a real polynomial defined on ℝⁿ with P(0) = 0. We prove that convolution with Kexp(i/P) is continuous on L²(ℝⁿ) with bounds depending only on K, n and the degree of P, but not on the coefficients of P.

On the oscillation of a class of linear homogeneous third order differential equations

N. Parhi, P. Das (1998)

Archivum Mathematicum

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In this paper we have considered completely the equation y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 , ( * ) where a ∈ C 2 ( [ σ , ∞ ) , R ) , b ∈ C 1 ( [ σ , ∞ ) , R ) , c ∈ C ( [ σ , ∞ ) , R ) and σ ∈ R such that a ( t ) ≤ 0 , b ( t ) ≤ 0 and c ( t ) ≤ 0 . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A.  C. Lazer earlier.