Spaces of functions of fractional smoothness on an irregular domain. (English. Russian original) Zbl 1068.46020

Besov, O. V.

Math. Notes 74, No. 2, 157-176 (2003); translation from Mat. Zametki 74, No. 2, 163-183 (2003).

Let \(G\) be an arbitrary domain in \(\mathbb{R}^n\). The paper deals with spaces of type \(B^s_{pq} (G)\), \(F^s_{pq} (G)\), where \(s>0\), \(1\leq p,q \leq \infty\), are characterised by integral representations, norms in terms of differences, and (equivalently) in terms of best approximations by polynomials. The main aim of this paper is to study the embedding \[ B^s_{pp} (G) \hookrightarrow L_q (G), \quad 1<p<q< \infty, \] subject to the quality of the irregular domain \(G\).

Reviewer: Hans Triebel (Jena)

MSC:

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

Besov spaces in aribitrary domains; Triebel-Lizorkin spaces in arbitrary domains; embeddings