  In this paper we study the problem of deriving further Sobolev inequalities
from a given Sobolev inequality. We use several different methods, including
Bessel potentials and Riesz transforms. We apply the results to the Ricci flow
to extend the author's results on the $W^{1,2}$ Sobolev inequality along the
Ricci flow to $W^{1,p}$ and $W^{2,p}$ Sobolev inequalities for general p.
