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Traces of weighted function spaces: dyadic norms and Whitney extensions. (English) Zbl 1406.46024

The aim of the paper is to review the literature concerning trace spaces of various weighted smoothness spaces. The authors use the Whitney extension operator and consider the weights \(w_\alpha(x)= \min(1,|x_{d+1}|^\alpha)\), \(\alpha>1\) on \(\mathbb{R}^{d+1}_+\). The main results are the trace theorems for the following weighted spaces defined on \(\mathbb{R}^{d+1}_+\): first-order Sobolev spaces, Besov and Triebel-Lizorkin spaces of smoothness \(s\), \(0<s<1\). The characterization of the trace spaces based on averages on dyadic cubes is presented since this approach is well-adapted to the Whitney extension operator.

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B35 Function spaces arising in harmonic analysis
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
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