Singular integrals and commutators in generalized Morrey spaces

We consider a singular an integral operator K with a variable Calderon-Zygmund type kernel k(x:xi), x is an element of R-n, xi is an element of R-n\{0}, satisfying a mixed homogeneity condition of the form k(x:mu(n1)xi(1),...,mu(alpha n)xi(n)) = mu(-)Sigma(n)(i=1) (alpha i) k(x:xi), alpha 1 >= 1 and mu > 0. The continuity of this operator in L-p(R-n) is well studied by Fabes and Riviere. Our goal is to extend their result to generalized Morrey spaces L-p,L-w(R-n), p is an element of (1, infinity) with a weight w satisfying suitable dabbling and integral conditions. A special attentional is paid to the commutator L[a, k] = Ka-aK with the operator of multiplication by BMO functions.