Variable exponent trace spaces

Tom 183 / 2007

Lars Diening, Peter Hästö Studia Mathematica 183 (2007), 127-141 MSC: 46E30, 46E35. DOI: 10.4064/sm183-2-3


The trace space of $W^{1,p(\cdot)}(\mathbb{R}^n\times [0,\infty))$ consists of those functions on $\mathbb{R}^n$ that can be extended to functions of $W^{1,p(\cdot)}(\mathbb{R}^n\times [0,\infty))$ (as in the fixed-exponent case). Under the assumption that $p$ is globally $\log$-Hölder continuous, we show that the trace space depends only on the values of $p$ on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.


  • Lars DieningSection of Applied Mathematics
    Freiburg University
    Eckerstrasse 1
    79104 Freiburg/Breisgau, Germany
  • Peter HästöDepartment of Mathematical Sciences
    P.O. Box 3000
    FI-90014 University of Oulu, Finland

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