Regularity properties of singular integral operators
Studia Mathematica, Tome 119 (1996) no. 3, pp. 199-217
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For s>0, we consider bounded linear operators from $D(ℝ^n)$ into $D'(ℝ^n)$ whose kernels K satisfy the conditions $|∂^{γ}_{x}K(x,y)| ≤ C_{γ}|x-y|^{-n+s-|γ|}$ for x≠y, |γ|≤ [s]+1, $|∇_{y} ∂^{γ}_{x} K(x,y)| ≤ C_{γ}|x-y|^{-n+s-|γ|-1}$ 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.
@article{10_4064_sm_119_3_199_217,
author = {Abdellah Youssfi},
title = {Regularity properties of singular integral operators},
journal = {Studia Mathematica},
pages = {199--217},
publisher = {mathdoc},
volume = {119},
number = {3},
year = {1996},
doi = {10.4064/sm-119-3-199-217},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-119-3-199-217/}
}
TY - JOUR AU - Abdellah Youssfi TI - Regularity properties of singular integral operators JO - Studia Mathematica PY - 1996 SP - 199 EP - 217 VL - 119 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-119-3-199-217/ DO - 10.4064/sm-119-3-199-217 LA - en ID - 10_4064_sm_119_3_199_217 ER -
Abdellah Youssfi. Regularity properties of singular integral operators. Studia Mathematica, Tome 119 (1996) no. 3, pp. 199-217. doi: 10.4064/sm-119-3-199-217
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