Geodesic
$L^p({\Bbb R}^n)$ boundedness for the commutator of a homogeneous singular integral operator
Guoen Hu 1
1 Department of Applied Mathematics University of Information Engineering P.O. Box 1001-747, Zhengzhou 450002 People's Republic of China
Studia Mathematica, Tome 154 (2003) no. 1, pp. 13-27 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The commutator of a singular integral operator with homogeneous kernel ${\mit \Omega }(x)/|x|^n$ is studied, where ${\mit \Omega }$ is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that ${\mit \Omega }\in L(\mathop {\rm log}\nolimits L)^{k+1}(S^{n-1})$ is a sufficient condition for the $k$th order commutator to be bounded on $L^p({{\mathbb R}}^n)$ for all $1 p\infty $. The corresponding maximal operator is also considered.
DOI : 10.4064/sm154-1-2
Keywords: commutator singular integral operator homogeneous kernel mit omega studied where mit omega homogeneous degree zero has mean value zero unit sphere proved mit omega mathop log nolimits n sufficient condition kth order commutator bounded mathbb infty corresponding maximal operator considered

Guoen Hu  1

1 Department of Applied Mathematics University of Information Engineering P.O. Box 1001-747, Zhengzhou 450002 People's Republic of China 
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Guoen Hu. $L^p({\Bbb R}^n)$ boundedness for the commutator of a
 homogeneous singular integral operator. Studia Mathematica, Tome 154 (2003) no. 1, pp. 13-27. doi: 10.4064/sm154-1-2

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