JournalszaaVol. 19, No. 3pp. 763–779

Traces of Besov Spaces Revisited

  • J. Johnsen

    Aalborg Universitet, Denmark
Traces of Besov Spaces Revisited cover
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Abstract

For the trace of Besov spaces Bp,qsB^s_{p,q} onto a hyperplane, the borderline case with s=np(n1)s = \frac {n}{p} – (n–1) and 0<p<10 < p < 1 is analysed and a new dependence on the sum-exponent qq is found. Through examples the restriction operator defined for ss down to 1p\frac {1}{p}, and valued in LpL_p, is shown to be distinctly different and, moreover, unsuitable for elliptic boundary problems. All boundedness properties (both new and previously known) are found to be easy consequences of a simple mixed-norm estimate, which also yields continuity with respect to the normal coordinate. The surjectivity for the classical borderline s=1p(1p<)s = \frac {1}{p} (1 ≤ p < \infty) is given a simpler proof for all q]20,1]q \in ]20, 1], using only basic functional analysis. The new borderline results are based on corresponding convergence criteria for series with spectral conditions.

Cite this article

J. Johnsen, Traces of Besov Spaces Revisited. Z. Anal. Anwend. 19 (2000), no. 3, pp. 763–779

DOI 10.4171/ZAA/979