Variable exponent trace spaces
Volume 183 / 2007
Studia Mathematica 183 (2007), 127-141
MSC: 46E30, 46E35.
DOI: 10.4064/sm183-2-3
Abstract
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.
