Singular Integrals and Commutators in Generalized Morrey Spaces

We consider a singular an integral operator K with a variable Calderón-Zygmund typekernel k（x;ξ）,x ∈ R~n,ξ∈ R~n\{0},satisfying a mixed homogeneity condition of the form k(x;μα1ξ1,…,μα_nξn)=μ-Σi~n=1αik（x;ξ）,αi≥1 and μ>0.The continuity of this operator in Lp（R~n）is well studiedby Fabes and Rivière.Our goal is to extend their result to generalized Morrey spaces Lp,w（R~n）,p ∈（1,∞）with a weight ω satisfying suitable dabbling and integral conditions.A special attention ispaid to the commutator l[a,k]=Ka-aK with the operator of multiplication by BMO functions.