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42-XX Harmonic analysis on Euclidean spaces
42Axx Harmonic analysis in one variable
42A50 Conjugate functions, conjugate series, singular integrals

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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

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.

$L^{2}$ Estimates for Oscillatory Integrals

G. Sampson (1998)

Colloquium Mathematicae

Lp bounds for Hilbert transforms along convex curves.

A. Cordoba, A. Nagel, J. Vance (1986)

Inventiones mathematicae

Currently displaying 1 – 3 of 3