engleski

A note on the trace theorem for Besov-type spaces of generalized smoothness on d-sets

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.

Function spaces of generalized smoothness ; d-sets ; trace space ; Bernstein functions

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