Variable exponent trace spaces

Abstract. The trace space of W 1,p(·)(Rn × [0,∞)) consists of those functions on Rn that can be extended to functions of W 1,p(·)(Rn × [0,∞)) (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. 1