Geodesic
Lp -Boundedness of a Singular Integral Operator
Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 404-412

Voir la notice de l'article provenant de la source Cambridge University Press

Let $b(t)$ be an ${{L}^{\infty }}$ function on $\mathbf{R}$ , $\Omega ({y}')$ be an ${{H}^{1}}$ function on the unit sphere satisfying the mean zero property (1) and ${{Q}_{m}}(t)$ be a real polynomial on $\mathbf{R}$ of degree $m$ satisfying ${{Q}_{m}}(0)\,=\,0$ . We prove that the singular integral operator $${{T}_{Qm,}}b\left( f \right)\left( x \right)=p.v.\int\limits_{\mathbf{R}}^{n}{b\left( \left| y \right| \right)}\Omega \left( y \right){{\left| y \right|}^{-n}}f\left( x-{{Q}_{m}}\left( \left| y \right| \right){y}' \right)\,\,dy$$ is bounded in ${{L}^{p}}({{\mathbf{R}}^{n}})$ for $1 , and the bound is independent of the coefficients of ${{Q}_{m}}(t)$ .
DOI : 10.4153/CMB-1998-054-5
Mots-clés : 42B20, singular integral, rough kernel, Hardy space 
Al-Hasan, Abdelnaser J.; Fan, Dashan. Lp -Boundedness of a Singular Integral Operator. Canadian mathematical bulletin, Tome 41 (1998) no. 4, pp. 404-412. doi: 10.4153/CMB-1998-054-5
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     title = {Lp {-Boundedness} of a {Singular} {Integral} {Operator}},
     journal = {Canadian mathematical bulletin},
     pages = {404--412},
     year = {1998},
     volume = {41},
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     doi = {10.4153/CMB-1998-054-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-054-5/}
}
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