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

Pan, Yibiao; Sampson, Gary; Szeptycki, Paweł

L^{2}

and

L^{p}

estimates for oscillatory integrals and their extended domains

Pan, Yibiao ; Sampson, Gary ; Szeptycki, Paweł

Studia Mathematica, Tome 122 (1997), p. 201-224 / Harvested from The Polish Digital Mathematics Library

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Résumé

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.

Publié le : 1997-01-01

Zbl 0876.42008

EUDML-ID : urn:eudml:doc:216372

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     author = {Yibiao Pan and Gary Sampson and Pawe\l\ Szeptycki},
     title = {$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {201-224},
     zbl = {0876.42008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv122i3p201bwm}
}

Pan, Yibiao; Sampson, Gary; Szeptycki, Paweł. $L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains. Studia Mathematica, Tome 122 (1997) pp. 201-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i3p201bwm/

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