Extrapolation of operators defined on domains and boundary respecting Ap weights

We formulate a Rubio de Francia type extrapolation theorem on domains Omega in R-n. The machinery required is a pair of local A(p) weight classes that give rise to an appropriately defined maximal operator bounded on weighted L-p spaces. The definitions we give of the local A(p) classes respect the shape of the boundary of Omega and, in addition, one class of weights can be easily seen to contain superharmonic functions.