Commutators generated by singular integral operators with variable kernels and local Campanato functions on generalized local Morrey spaces. (English) Zbl 1341.42030

Mo, Huixia; Xue, Hongyang

Commun. Math. Anal. 19, No. 2, 32-42 (2016).

Summary: In this paper, we obtain the boundedness for the singular integral operator with rough variable kernel \(T_\Omega\) on the generalized local Morrey spaces, as well as the boundedness for the multilinear commutators generated by \(T_\Omega\) and local Campanato functions.

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25	Maximal functions, Littlewood-Paley theory
42B35	Function spaces arising in harmonic analysis

Keywords:

singular integral operators; variable kernels; commutators; local Campanato functions; generalized local Morrey spaces