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 Ω f x = p.v. Z 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 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. Keywords: Higher order = mth order commutator operators, rough kernel, A p s0 weight, generalized weighted Morrey space.

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