Sobolev Inequalities, Riesz Transforms, and the Ricci Flow

A number of results about deriving further Sobolev inequalities from a given Sobolev inequality are presented.Various techniques are employed,including Bessel potentials and Riesz transforms.Combining these results with theW1,2 Sobolev inequality along the Ricci flow established by the author in earlier papers then yields various new Sobolev inequalities along the Ricci flow.