$L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions

G. Sampson

L^{p}

type mapping estimates for oscillatory integrals in higher dimensions

G. Sampson

Studia Mathematica, Tome 173 (2006), p. 101-123 / Harvested from The Polish Digital Mathematics Library

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Résumé

We show in two dimensions that if $K f = \int_{ℝ ₊ ²} k (x, y) f (y) d y$ , $k (x, y) = (e^{i x^{a} \cdot y^{b}}) {/ (| x - y |}^{η})$ , p = 4/(2+η), a ≥ b ≥ 1̅ = (1,1), $v_{p} (y) = y^{(p / p^{'}) (1 ̅ - b / a)}$ , then ${| | K f | |}_{p} {\leq C | | f | |}_{p, v_{p}}$ if η + α₁ + α₂ < 2, $α_{j} = 1 - b_{j} / a_{j}$ , j = 1,2. Our methods apply in all dimensions and also for more general kernels.

Publié le : 2006-01-01

Zbl 1098.42010

EUDML-ID : urn:eudml:doc:285278

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     title = {$L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions},
     journal = {Studia Mathematica},
     volume = {173},
     year = {2006},
     pages = {101-123},
     zbl = {1098.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-1}
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G. Sampson. $L^{p}$ type mapping estimates for oscillatory integrals in higher dimensions. Studia Mathematica, Tome 173 (2006) pp. 101-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-1/