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Turkish Journal of Mathematics

Authors

JAIRO VILLEGAS

DOI

-

Abstract

In this paper we aim to extend a result of Hörmander's, that \mathcal{B}_{p,k}^{loc}(\Omega)\subset\mathcal{C}^m(\Omega) if \frac{(1+\left \cdot\right )^m}{k}\in L_{p^\prime}, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space \bigcap_{j=1}^\infty\mathcal{B}_{p_j,k_j}^{loc} (\Omega, E) (1\leq p_j\leq\infty, k_j=e^{j\omega}, j=1,2,\dots) is topologically isomorphic to \mathcal{E}_\omega(\Omega, E ). Moreover, it is well known that the union of Sobolev spaces \mathcal{H}_{s}^{loc}(\Omega) (=\mathcal{B}_{2,(1+ \cdot ^2)^{s/2}}^{loc}(\Omega)) coincides with the space \mathcal{D}^{\prime\,F}(\Omega) of finite order distributions on \Omega. We show that this is also verified in the context of vector valued Beurling ultradistributions.

First Page

387

Last Page

398

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