Hello,

It seems that there is no English translation of the Schwartz's book 1966. I may need to use the spaces like

$$ \dot{\mathcal{B}}(R),\quad \dot{\mathcal{B}}'(R),\quad \mathcal{B}(R),\quad \mathcal{B}'(R),\quad D_{L^p}(R),\quad D_{L^p}'(R) $$ etc.

I have never seen any English references on these spaces. Does anyone know one?

EDIT:

For example, $f\in D_{L^p}(R)$ if and only if $f$ is a smooth function such that it, together with all its derivatives, belongs to $L^p(R)$. $D_{L^p}'(R)$ is its dual.

$\mathcal{B}(R)=D_{L^\infty}(R)$, and $\mathcal{B}'(R)$ is its dual.

Thank you very much!

Anand