For the trace of Besov spaces onto a hyperplane, the borderline case with and is analysed and a new dependence on the sum-exponent is found. Through examples the restriction operator defined for down to , and valued in , 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 is given a simpler proof for all , 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. 763–779DOI 10.4171/ZAA/979