Local spaces of distributions
Abstract
A space of distributions E is local if, roughly, a distribution T belongs to E whenever T belongs to E in the neighborhood of every point. A space E, in whose definition growth conditions enter, is not local but one can associate with E a local space
. This is classical for the spaces
[6], and was done for the Sobolev spaces
by Laurent Schwartz in his 1956 Bogotà lectures [8], where he presented an expository account of B. Malgrange's doctoral dissertation. In the present paper I establish some simple properties of the space
attached to a space of distributions E. To a distribution space E we can also attach the space E, consisting of those elements of E which have compact support. At the end of the paper I make some remarks concerning the duality between local spaces and spaces of distributions with compact support.
![E_{loc}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/dd888d47378d1bc62f132dd97c21903b.png)
![L<sup>p</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/7b9dabe4a872a8aaf123760be1ed9a11.png)
![\mathcal H<sup>5</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/473c314bf6030ef5345f48264add90d3.png)
![E_{loc}](http://siba-ese.unile.it/plugins/generic/latexRender/cache/dd888d47378d1bc62f132dd97c21903b.png)
DOI Code:
10.1285/i15900932v11p215
Full Text: PDF