On the behaviors of a class of singular type rough higher order commutators on generalized weighted morrey spaces

Abstract

In this paper, we study the boundedness of a class of singular type rough higher order commutators defined by T A,m ? f(x) = p.v. Z Rn ?(x ? y) |x ? y| n (A (x) ? A (y))m f(y)dy and MA,m ? f(x) = sup r>0 1 r n Z |x?y| 1) is a homogeneous function of degree 0 on R n and satisfies the integral zero property over the unit sphere S n?1 on generalized weighted Morrey spaces, respectively. As an application, we get the boundedness of these operators on weighted Morrey spaces, respectively.