TRANSLATION INVARIANT PROJECTIONS IN SOBOLEV SPACES ON TORI IN THE L1 AND UNIFORM NORMS

The idempotent multipliers on Sobolev spaces on the torus in the L1 and uniform norms are characterized in terms of the coset ring of the dual group of the torus. This result is deduced from a more general theorem concerning certain translation invariant subspaces of vector-valued function spaces on tori.