  The present paper deals with singular integrals with variable
Caldero'n-Zygmund type kernels satisfying mixed homogeneity condition. The
continuity of these operators in The Lebesgue spaces is well studied by Fabes
and Rivie're. Our goal is to extend their results in generalized Morrey spaces
with weight satisfying suitable dabbling and integral conditions. A special
attention is paid also of the commutators of the kernel with functions of
bounded or vanishing mean oscillation.
