Weighted inequalities for some integral operators with rough kernels

Abstract

In this paper we study integral operators with kernels K(x, y) = k1(x − A1y)...km(x − Amy), ki(x) = Ωi(x) |x|n/qi where Ωi : Rn → R are homogeneous functions of degree zero, satisfying a size and a Dini condition, Ai are certain invertible matrices, and n q1 + . . . n qm = n − α, 0 ≤ α < n. We obtain the appropriate weighted Lp − Lq estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.