×

Commutators of convolution operators. (Chinese. English summary) Zbl 1019.42007

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.

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
PDFBibTeX XMLCite