  In this paper, we study maximal functions along some finite type curves and
hypersurfaces. In particular, various impacts of non-isotropic dilations are
considered. Firstly, we provide a generic scheme that allows us to deduce the
sparse domination bounds for global maximal functions under the assumption that
the corresponding localized maximal functions satisfy the $L^{p}$ improving
properties. Secondly, for the localized maximal functions with non-isotropic
dilations of curves and hypersurfaces whose curvatures vanish to finite order
at some points, we establish the $L^{p}\rightarrow L^{q}$ bounds $(q >p)$. As a
corollary, we obtain the weighted inequalities for the corresponding global
maximal functions, which generalize the known unweighted estimates.
