As I am relatively new to these matters, I would like to know if you could provide me a reference for Besov spaces on unbounded domains, because when I checked the first tome of Triebel's Theory of Function Spaces, I only found the case of a smooth bounded set aside of whole or half space (in Bergh's Interpoation spaces, there is no mention neither of these spaces).
Hormander: The Analysis of Linear Partial Differential Operators II, 1983, page 13 ff.
These spaces are $B_{k,p}(\mathbb R^n)\cap \mathcal E'(X)$, where $X$ is open in $\mathbb R^n$.
O.V Besov, V.P Il'in, S.M Nikolskii. Integral Representations of Functions and Embedding Theorems. Most of results are stated for arbitrary domains $G\subset \mathbb R^n$.

$\begingroup$ Thank you very much Andrew, I didn't accept your answer because I can only accept one, but I really appreciate the extra reference. I didn't know Besov himself wrote about the subject; sometimes in Analysis, there are pioneers who don't write about their own work, e.g. Calderón. $\endgroup$ – PaulBenjamin Apr 18 '15 at 17:20
The following papers may help:
 "Besov Spaces on Domains in $\mathbb{R}^d$" by R. Devore and R. Sharpley
This paper is for Besov spaces $B^{\alpha}_{q}(L_p(\Omega)),~p,q,\alpha \in (0,\infty )$ on domains $\Omega\subset \mathbb{R}^d$
http://www.ams.org/journals/tran/199333502/S00029947199311523216/S00029947199311523216.pdf
 "Elliptic and parabolic problems in unbounded domains" by Patrick Guidotti
This examines general existence and regularity results in Besov spaces (specifically, on unbounded domains $\mathbb{R}^n\times\Omega$).

$\begingroup$ Thank you very much Mr Simpson, this is a good complementary reference that you added here, as Hörmander's treatment of the subject does not include the Besov spaces of three parameters. $\endgroup$ – PaulBenjamin Jul 24 '15 at 10:56

$\begingroup$ No problem. I am quite interested in Besov spaces. $\endgroup$ – user71046 Jul 24 '15 at 10:57