We use an isomorphism established by Langenbruch between some sequence spaces and weighted spaces of generalized functions to give sufficient conditions for the (Beurling type) space $CBs_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $omega$ satisfying the mild condition: $2omega(t)leq omega(Ht)+H$ for some $H>1$ and for all $tgeq0$, the space $CBs_omega$ in the sense of Bj"orck is also nuclear.
About the nuclearity of $mathcal{S}_{(M_{p})}$ and $mathcal{S}_{omega}$
Alessandro Oliaro
2020-01-01
Abstract
We use an isomorphism established by Langenbruch between some sequence spaces and weighted spaces of generalized functions to give sufficient conditions for the (Beurling type) space $CBs_{(M_p)}$ to be nuclear. As a consequence, we obtain that for a weight function $omega$ satisfying the mild condition: $2omega(t)leq omega(Ht)+H$ for some $H>1$ and for all $tgeq0$, the space $CBs_omega$ in the sense of Bj"orck is also nuclear.
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