Calderon-Zygmund operators with kernels of Dini's type on generalized weighted variable exponent Morrey spaces

Let T be a Calderon-Zygmund operator of type omega with omega(t) being nondecreasing and satisfying a kind of Dini's type condition and let T-(b) over right arrow be the multilinear commutators of T with BMOm functions. In this paper, we study the boundedness of the operators T and T-(b) over right arrow on generalized weighted variable exponent Morrey spaces M-p(.),M-phi(w) with the weight function w belonging to variable Muckenhoupt's class A(p(.))(R-n). We find the sufficient conditions on the pair (phi(1), phi(2)) with (b) over right arrow is an element of BMOm(R-n) which ensures the boundedness of the operators T and T-(b) over right arrow from M-p(.),M-phi 1(w) to M-p(.),M-phi 2(w).