Regularity properties of singular integral operators

Youssfi, Abdellah

Studia Mathematica, Tome 119 (1996), p. 199-217 / Harvested from The Polish Digital Mathematics Library

Résumé

For s>0, we consider bounded linear operators from $D (ℝ^{n})$ into $D^{'} (ℝ^{n})$ whose kernels K satisfy the conditions $| \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ |}$ for x≠y, |γ|≤ [s]+1, $| \nabla_{y} \partial_{x}^{γ} K (x, y) | \leq C_{γ} {| x - y |}^{- n + s - | γ | - 1}$ for |γ|=[s], x≠y. We establish a new criterion for the boundedness of these operators from $L^{2} (ℝ^{n})$ into the homogeneous Sobolev space $Ḣ^{s} (ℝ^{n})$ . This is an extension of the well-known T(1) Theorem due to David and Journé. Our arguments make use of the function T(1) and the BMO-Sobolev space. We give some applications to the Besov and Triebel-Lizorkin spaces as well as some other potential spaces.

Publié le : 1996-01-01

Zbl 0857.42008

EUDML-ID : urn:eudml:doc:216296

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     author = {Abdellah Youssfi},
     title = {Regularity properties of singular integral operators},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {199-217},
     zbl = {0857.42008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv119i3p199bwm}
}

Youssfi, Abdellah. Regularity properties of singular integral operators. Studia Mathematica, Tome 119 (1996) pp. 199-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv119i3p199bwm/

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