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

We mainly show that for a conformal metric g=u^4{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.