Glasnik Matematicki, Vol. 54, No. 1 (2019), 233-254.

A NOTE ON THE TRACE THEOREM FOR BESOV-TYPE SPACES OF GENERALIZED SMOOTHNESS ON D-SETS

Vanja Wagner

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: wagner@math.hr

Abstract.   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 ⊂ℝn, d≤ n. The proof closely follows the classical approach by Jonsson, Wallin in [18] 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.

2010 Mathematics Subject Classification.   46E35, 60J75, 60G51

Key words and phrases.   Function spaces of generalized smoothness, d-sets, trace space, Bernstein functions

Full text (PDF) (free access)

https://doi.org/10.3336/gm.54.1.10

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