On the weak (1,1) boundedness of a class of oscillatory singular integrals

Pan, Yibiao

Pan, Yibiao

Studia Mathematica, Tome 104 (1993), p. 279-287 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include $ϕ (x) = e^{- 1 / x^{2}}$ and $ϕ (x) = x e^{- 1 / | x |}$ . Some related counterexample is also discussed.

Publié le : 1993-01-01

Zbl 0812.42011

EUDML-ID : urn:eudml:doc:216017

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     author = {Yibiao Pan},
     title = {On the weak (1,1) boundedness of a class of oscillatory singular integrals},
     journal = {Studia Mathematica},
     volume = {104},
     year = {1993},
     pages = {279-287},
     zbl = {0812.42011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p279bwm}
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Pan, Yibiao. On the weak (1,1) boundedness of a class of oscillatory singular integrals. Studia Mathematica, Tome 104 (1993) pp. 279-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p279bwm/

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