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. $\endgroup$ – Paul-Benjamin 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 $\Omega\subset \mathbb{R}^d$


  • "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. $\endgroup$ – Paul-Benjamin Jul 24 '15 at 10:56
  • $\begingroup$ No problem. I am quite interested in Besov spaces. $\endgroup$ – user71046 Jul 24 '15 at 10:57

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.