Variable exponent trace spaces

The trace space of W-1,W-p(.)(R-n x [0,infinity)) consists of those functions on R-n that can be extended to functions of W-1,W-p(.) (R-n x [0, infinity)) (as in the fixed-exponent case). Under the assumption that p is globally log-Holder 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.