References dealing with function spaces in pde like $C^k(\mathbb R^n)$, $C^\infty_c(\mathbb R^n), \ldots$?

Question

What would be nice references for function spaces like $C^k(\mathbb R^n$), $C_0(\mathbb R^n)$, $C^\infty_c(\mathbb R^n), \ldots$ and most common function spaces which are offen employed in partial differential equations?

I'm looking references that deal with completeness, density, etc., more generally, the functional analytic aspects of those kind of spaces.

References for function spaces on manifolds would be also wellcome.

Thanks!

Answer 1

I believe Lars Hormander's first volume of The Analysis of Partial Differential Operators covers relevant material to your first reference request. You might try Hans Triebel's Theory of Function Spaces also.