摘要
We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.
We consider a singular an integral operator K with a variable Calderón-Zygmund type kernel k（x; ξ）, x ∈R^n, ξ∈ R^n／{0}, satisfying a mixed homogeneity condition of the form k（x; μ^α1ξ1,..., μ^αnξn） =μ^-∑i=1^n α≥1 k（x, ξ）, αi≥ 1 and μ 〉 0. The continuity of this operator in L^（^＇＇） is well studied by Fabes and Rivière. Our goal is to extend their result to generalized Morrey spaces L^p,ω（R^n）, p ∈ （1, ∞） with a weight w satisfying suitable dabbling and integral conditions. A special attention is paid to the commutator C[α, k]=Kα- αK with the operator of multiplication by BMO functions.
