Hu, Guoen; Lu, Shanzhen; Ma, Bolin Commutators of convolution operators. (Chinese. English summary) Zbl 1019.42007 Acta Math. Sin. 42, No. 2, 359-368 (1999). By reducing the problem to a local one and using the Fourier transform estimates, the authors obtain the \(L^p(\mathbb R^n)\) boundedness for some \(p\in (1,\infty)\) of some operators related to the commutators of convolution operators with BMO functions. As applications, the authors establish the \(L^p(\mathbb R^n)\) boundedness for the discrete maximal commutator of the spherical means operator with any BMO function and commutators of singular integral operators on low dimensional manifolds with BMO functions. Reviewer: Yang Dachun (Beijing) Cited in 3 Documents MSC: 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) 47B47 Commutators, derivations, elementary operators, etc. 42B25 Maximal functions, Littlewood-Paley theory 47A30 Norms (inequalities, more than one norm, etc.) of linear operators Keywords:convolution operator; commutator; maximal operator; boundedness; BMO PDFBibTeX XMLCite \textit{G. Hu} et al., Acta Math. Sin. 42, No. 2, 359--368 (1999; Zbl 1019.42007)