You will find here a preprint entitled "Some inequalities in weighted Sobolev spaces", which I wrote in 1987. The work here was motivated by an attempt to provide justification for the positive energy theorem a la Witten. I have never attempted to publish it, because, once the work here was completed, I have discovered the paper by Robert Bartnik, The mass of an asymptotically flat manifold, Comm. Pure Appl. Math. 39 (1986), pp. 661--693, where some of the inequalities proved here have also been established. The methods here are different from Bartnik's, and they can be used to prove more general inequalities than those presented; for example, from Lemma 1 one immediately obtains McKean's inequality on hyperbolic space.

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