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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