Singular Integrals and Commutators in Generalized Morrey Spaces

Abstract

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.

LaTeX, 19 pages; corrected typos

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