Weighted Valuable Maximal Inequalities of Fefferman-Stein on Non-Homogeneous Spaces

In terms of the results of Y.Sawano and the duality theory, the authors give the Fefferman-Stein weighted valuable maximal inequalities on non-homogeneous space that generalize the results of K.F.Andersen and R.T.John. Meanwhile, the idea is also right when it comes to the valuable maximal inequalities on Euclidean space.