In this expository article we present the characterizations proved by J. Chung, S.-Y. Chung and D. Kim, and by S.-Y. Chung, D. Kim and S. Lee, of the Schwartz space 𝔖 and of the Beurling-Björck Space 𝔖ω. For the most part we follow the original proofs, only adjusting the estimates and necessary in order to prove not only set-theoretic equalities, but also topological equalities. These results show that space 𝔖ω is, as a set as well as topologically, a direct generalization of the space 𝔖. Minor modifications of the original arguments allow us to obtain explicit linear estimates.
@article{1559,
title = {Characterizations of the Schwartz Space and the Beurling-Bjorck Space So},
journal = {CUBO, A Mathematical Journal},
volume = {6},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/1559}
}
Alvarez, Josefina; Obiedat, Hamed M. Characterizations of the Schwartz Space and the Beurling-Björck Space 𝔖ω. CUBO, A Mathematical Journal, Tome 6 (2004) 17 p. http://gdmltest.u-ga.fr/item/1559/