Algebra Of Product Calderón-Zygmund Operators Associated To Para-Accretive Functions

Han[11]et al proved that all classical Calderon-Zygmund operators satisfying T(b)=T*(b)=0 forms an algebra,where b is a para-accretive function.In this article,a similar result is proved for product singular integral operator in Journé’s class.More precisely,applying Calderon’s reproducing formulas and almost orthogonal estimates associated to para-accretive functions,we obtain that all product singular integral operator in Journé’s class with T1(b1)=T1*(b1)=T2(b2)=T2*(b2)=0 forms an algebra,where b1,b2 are para-accretive functions.