2018/03/27 by Vanja Wagner, Wagner, Vanja
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA
paper · pdf · doi:10.48550/arxiv.1803.09986
Previously part of the appendix of publication arXiv:1608.01384
arxiv created 2018/03/27 · arxiv updated 2018/03/28
The main goal of this paper is to give a complete proof of the trace theorem for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling conditions on d-sets D⊂\mathbb Rn, d≤ n. The proof closely follows the classical approach by Jonsson and Wallin and the trace theorem for classical Besov spaces. Here, the trace space is defined by means of differences. When d=n, as an application of the trace theorem, we give a condition under which the test functions Cc^∞(D) are dense in the trace space on D.