  We define a scale of weighted Morrey spaces which contains different weighted
versions appearing in the literature. This allows us to obtain weighted
estimates for operators in a unified way. In general, we obtain results for
weights of the form $|x|^\alpha w(x)$ with $w\in A_p$ and nonnegative $\alpha$.
We study particularly some properties of power-weighted spaces and in the case
of the Hardy-Littlewood maximal operator our results for such spaces are sharp.
By using extrapolation techniques the results are given in abstract form in
such a way that they are automatically obtained for many operators.
