International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 756834, 9 pages
doi:10.1155/2008/756834
Research Article
Structure Theorem for Functionals in the Space Sω1,ω2′
Department of Mathematics, Hashemite University, P.O. Box 150459, Zarqa 13115, Jordan
Received 19 August 2007; Revised 30 September 2007; Accepted 22 November 2007
Academic Editor: Manfred H. Moller
Copyright © 2008 Hamed M. Obiedat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.