$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains
Studia Mathematica, Tome 122 (1997) no. 3, pp. 201-224
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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:
$L^p$ boundedness, oscillatory integrals, extended domains, Calderón-Zygmund kernels
Affiliations des auteurs :
Yibiao Pan 1 ; 1 ; 1
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Yibiao Pan; ; . $L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains. Studia Mathematica, Tome 122 (1997) no. 3, pp. 201-224. doi: 10.4064/sm-122-3-201-224
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