Sobolev Algebra Counterexamples

by Thierry Coulhon, Luke G. Rogers

In the Euclidean setting the Sobolev spaces $$W^{α,p}\cap L^\infty$$ are algebras for the pointwise product when α>0 and p∈(1,∞). This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices α,p.

Arxiv prepint version

Published version in JFG