Distributions supported in a hypersurface and local ℎ^{𝑝}

Abstract

We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space h p ( R n ) h^p(\mathbf {R}^n) . We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain Ω ⊂ R n \Omega \subset \mathbf {R}^n .