Estimates with global range for oscillatory integrals with concave phase

Bjorn Gabriel Walther

Colloquium Mathematicae, Tome 91 (2002), p. 157-165 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the maximal function $| | (S^{a} f) [x] {| |}_{L^{\infty} [- 1, 1]}$ where $(S^{a} f) {(t)}^{\land} (ξ) = e^{{i t | ξ |}^{a}} f ̂ (ξ)$ and 0 < a < 1. We prove the global estimate $| | S^{a} f {| |}_{L ² (ℝ, L^{\infty} [- 1, 1])} {\leq C | | f | |}_{H^{s} (ℝ)}$ , s > a/4, with C independent of f. This is known to be almost sharp with respect to the Sobolev regularity s.

Publié le : 2002-01-01

Zbl 1005.42008

EUDML-ID : urn:eudml:doc:283522

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     author = {Bjorn Gabriel Walther},
     title = {Estimates with global range for oscillatory integrals with concave phase},
     journal = {Colloquium Mathematicae},
     volume = {91},
     year = {2002},
     pages = {157-165},
     zbl = {1005.42008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-1}
}

Bjorn Gabriel Walther. Estimates with global range for oscillatory integrals with concave phase. Colloquium Mathematicae, Tome 91 (2002) pp. 157-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-2-1/