L contractive projections and the heat semigroup for differential forms
Robert S. Strichartz · Journal of Functional Analysis · 1986
A projection operator that is contractive on Lp for two distinct values of p is shown to be contractive for all values of p, and the range must be of a special form. This result is used to show that the heat semigroup for k-forms on many manifolds with nontrivial cohomology in dimension k cannot be contractive on any Lp for p ≠ 2.