We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{ p_{ 0}}(w), for all "flat" weights, w in A_{ p_{ 0}}, 1 < p_{ 0} <\infty, then for p in some small neighborhood around p_{ 0}, and all "flat" A_{ p} weights, w, the operator is weakly bounded on L^{ p}(w), and as a result we get strong type estimates for the operator.
Categories: math.CA