||Let µ be a Borel measure on Rd which may be non doubling. The only condition that µ must satisfy is µ(B(x, r)) ≤ Crn for all x Î Rd, r > 0 and for some fixed n with 0 < n ≤ d. In this paper we introduce a maximal operator N, which coincides with the maximal Hardy-Littlewood operator if µ(B(x, r)) ≈ rn for x Î supp(µ), and we show that all n-dimensional Calderón-Zygmund operators are bounded on Lp(w dµ) if and only if N is bounded on Lp(w dµ), for a fixed p Î (1, ∞). Also, we prove that this happens if and only if some conditions of Sawyer type hold. We obtain analogous results about the weak (p,p) estimates. This type of weights do not satisfy a reverse Hölder inequality, in general, but some kind of self improving property still holds. On the other hand, if Î RBMO(µ) and ε > 0 is small enough, then eεf belongs to this class of weights.