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


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DOI: 10.3336/gm.54.1.10


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