On the positivity of the Q-curvatures of the conformal metrics

We mainly show that for a conformal metric g=u4/n-2m|dx|² on Rⁿ with n≥ 2m+1, if the higher order Q-curvature Q⁽²ᵐ⁾g is positive and has slow decay near infinity, the lower order Q-curvature Q⁽²⁾g and Q⁽⁴⁾g are both positive if m is at least two.