A characterization of commutators for parabolic singular integrals

• Autores: Yanping Chen, Yong Ding
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 108, Nº 1, 2011, págs. 5-25
• Idioma: inglés
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• Resumen

  • In this paper, the authors give a characterization of the Lp-boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if b∈BMOφ(Rn,ρ), then the commutator [b,T] is a bounded operator from Lp(Rn) to the Orlicz space Lψ(Rn), where the kernel function Ω has no any smoothness on the unit sphere Sn−1. Conversely, if assuming on Ω a slight smoothness on Sn−1, then the boundedness of [b,T] from Lp(Rn) to Lψ(Rn) implies that b∈BMOφ(Rn,ρ). The results in this paper improve essentially and extend some known conclusions.