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

Yibiao Pan; Gary Sampson; Paweł Szeptycki

ArticleOriginal scientific text

Title

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

Authors ¹, ², ³

Affiliations

Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.
Department of Mathematics, University of Kansas Lawrence, Kansas 66044, U.S.A.

Abstract

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.

Keywords

ENG

L^{p}

boundedness, oscillatory integrals, extended domains, Calderón-Zygmund kernels

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Title

L2 and Lp estimates for oscillatory integrals and their extended domains

Affiliations

Abstract

Keywords

Bibliography

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