$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains
Volume 122 / 1997
Studia Mathematica 122 (1997), 201-224
DOI: 10.4064/sm-122-3-201-224
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.
