International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 756834, 9 pages
doi:10.1155/2008/756834

Structure Theorem for Functionals in the Space Sω1,ω2′

Abstract

We introduce the space Sω1,ω2 of all C∞ functions ϕ such that sup|α|≤m‖ekω1∂αϕ‖∞ and sup|α|≤m‖ekω2∂αϕ^‖∞ are finite for all k∈ℕ0, α∈ℕ0n, where ω1 and ω2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space Sω1,ω2 without conditions on the derivatives. For functionals in the dual space Sω1,ω2′, we prove a structure theorem by using the classical Riesz representation thoerem.