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1997 | 122 | 3 | 201-224
Tytuł artykułu

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

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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.
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.,
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