Distributional boundary values of generalized Hardy functions in Beurling’s tempered distributions

Let B be a proper open subset in ∝N and C be an open convex cone in ℝN. We define a generalization of the spaces of Hardy functions, Gpω,A (TB), 1 ≤ p ℞ ℞, and extended tempered distributions, S′ω, of Beurling’s tempered distributions, S′(ω). We obtain the analytical and topological properties of S′ω and show that the functions in Gpω,A (TC) 1 < p ≤ 2, have distributional boundary values in the weak topology of S′(ω) using the analytical properties of S′ω.