$L^{p}(ℝⁿ)$ boundedness for the commutator of a homogeneous singular integral operator

• Autorzy: Guoen Hu
• Języki publikacji: EN

Abstrakty

EN

The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that $Ω ∈ L(log L)^{k+1}(S^{n-1})$ is a sufficient condition for the kth order commutator to be bounded on $L^{p}(ℝⁿ)$ for all 1 < p < ∞. The corresponding maximal operator is also considered.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 154
• Numer: 1
• Strony: 13-27

Daty

wydano

2003

Twórcy

autor

Guoen Hu

• Department of Applied Mathematics, University of Information Engineering, P.O. Box 1001-747, Zhengzhou 450002, People's Republic of China

Identyfikatory

DOI

10.4064/sm154-1-2