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

Yıl 2018, Cilt: 8 Sayı: 1.1, 208 - 219, 01.09.2018

F. Gürbüz

Öz

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.

Kaynakça

• Bajsanski,B. and Coifman,R., (1966), On singular integrals, Proc. Sympos. Pure Math. Chicago, Illinois, X, pp.1-17.
• Calder´on,A.P., (1965), Commutators of singular integral operators, Proc. Nat. Acd. Sci. USA, 53, pp.1092-1099.
• Cohen,J. and Gosselin,J., (1986), A BM O estimate for multilinear singular integrals, Illinois J. Math., 30, pp.445-464.
• Guliyev,V.S., (2012), Generalized weighted Morrey spaces and higher order commutators of sublinear operators, Eurasian Math. J., 3, 3, pp.33-61.
• G¨urb¨uz,F., (2017), Sublinear operators with rough kernel generated by Calder´on-Zygmund operators and their commutators on generalized Morrey spaces, Math. Notes, 101, 3, pp.429-442.
• G¨urb¨uz,F., (2018), On the behaviors of sublinear operators with rough kernel generated by Calder´on- Zygmund operators both on weighted Morrey and generalized weighted Morrey spaces, Int. J. Appl. Math. & Stat., 57, 2 , pp.33-42.
• Komori,Y. and Shirai,S., (2009), Weighted Morrey spaces and a singular integral operator, Math. Nachr., 282, 2, pp.219-231.
• Iida,T., (2016), Weighted estimates of higher order commutators generated by BM O-functions and the fractional integral operator on Morrey spaces, J. Inequal. Appl., 4, pp.1-23.