A charaterization of commutators for parabolic singular integrals - Chen, Yanping; Ding, Yong (Mathematica Scandinavica, 2011)
In this paper, the authors give a characterization of the L^p-boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if bBMO_φ(R^n,ρ), then the commutator [b,T] is a bounded operator from L^p(R^n) to the Orlicz space L_ψ(R^n), where the kernel function Ω has no any smoothness on the unit sphere S^n-1. Conversely, if assuming on Ω a slight smoothness on S^n-1, then the boundedness of [b,T] from L^p(R^n) to L_ψ(R^n) implies that bBMO_φ(R^n,ρ). The results in this paper improve essentially and extend some known conclusions.