A note on Sobolev algebras
Robert S. Strichartz · Proceedings of the American Mathematical Society · 1971
Sufficient conditions are given for the Sobolev space $L_w^p = \{ f \in {L^p}({E^n}):{\mathfrak {F}^{ - 1}}(\hat f(\xi )w(\xi )) \in {L^p}\}$ to form an algebra under pointwise multiplication, when $1 \leqq p \leqq 2$. The conditions are verified for some examples.