  R. Jin showed that whenever A and B are sets of integers having positive
upper Banach density, the sumset A+B is piecewise syndetic. This result was
strengthened by Bergelson, Furstenberg, and Weiss to conclude that A+B must be
piecewise Bohr. We generalize the latter result to cases where A has Banach
density 0, giving a new proof of the previous results in the process.
