1Section of Applied Mathematics Freiburg University Eckerstrasse 1 79104 Freiburg/Breisgau, Germany 2Department of Mathematical Sciences P.O. Box 3000 FI-90014 University of Oulu, Finland
Studia Mathematica, Tome 183 (2007) no. 2, pp. 127-141
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.
Keywords:
trace space cdot mathbb times infty consists those functions mathbb extended functions cdot mathbb times infty fixed exponent under assumption globally log h lder continuous trace space depends only values boundary main result define intrinsic norm trace space terms sharp type operator
Affiliations des auteurs :
Lars Diening
1
;
Peter Hästö
2
1
Section of Applied Mathematics Freiburg University Eckerstrasse 1 79104 Freiburg/Breisgau, Germany
2
Department of Mathematical Sciences P.O. Box 3000 FI-90014 University of Oulu, Finland
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author = {Lars Diening and Peter H\"ast\"o},
title = {Variable exponent trace spaces},
journal = {Studia Mathematica},
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number = {2},
doi = {10.4064/sm183-2-3},
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Lars Diening; Peter Hästö. Variable exponent trace spaces. Studia Mathematica, Tome 183 (2007) no. 2, pp. 127-141. doi: 10.4064/sm183-2-3
