ON THE BEHAVIORS OF A CLASS OF SINGULAR TYPE ROUGH HIGHER ORDER COMMUTATORS ON GENERALIZED WEIGHTED MORREY SPACES

Özet

In this paper, we study the boundedness of a class of singular type rough higher order commutators defined by T A,m Ω f(x) = p.v. Rn Ω(x − y) |x − y| n (A (x) − A (y))m f(y)dy and MA,m Ω f(x) = sup r>0 1 rn |x−y| 1) is a homogeneous function of degree 0 on Rn and satisfies the integral zero property over the unit sphere Sn−1 on generalized weighted Morrey spaces, respectively. As an application, we get the boundedness of these operators on weighted Morrey spaces, respectively. Keywords: Higher order (= mth order) commutator operators, rough kernel, A p s weight, generalized weighted Morrey space.