  In this note we prove a trace theorem in fractional spaces with variable
exponents. To be more precise, we show that if $p\colon\overline{\Omega}\times
\overline{\Omega}\to (1,\infty)$ and $q:\partial \Omega \rightarrow (1,\infty)$
are continuous functions such that \[
  \frac{(n-1)p(x,x)}{n-sp(x,x)}>q(x)
  \qquad \mbox{in} \partial \Omega \cap
  \{x\in\overline{\Omega}\colon n-sp(x,x) >0\}, \] then the inequality $$
  \Vert f\Vert _{\scriptstyle L^{q(\cdot)}(\partial \Omega)}
  \leq C \left\{\Vert f\Vert _{\scriptstyle L^{\bar{p}(\cdot)}(\Omega)}+
  [f]_{s,p(\cdot,\cdot)} \right\} $$ holds. Here $\bar{p}(x)=p(x,x)$ and
$\lbrack f\rbrack_{s,p(\cdot,\cdot)} $ denotes the fractional seminorm with
variable exponent, that is given by
  \[
  \lbrack f\rbrack_{s,p(\cdot,\cdot)} :=
  \inf \left\{\lambda >0\colon
  \int_{\Omega}\int_{\Omega}\frac{|f(x)-f(y)|^{p(x,y)}}{\lambda ^{p(x,y)}
  |x-y|^{n+sp(x,y)}}dxdy<1\right\}
  \] and $\Vert f\Vert _{\scriptstyle L^{q(\cdot)}(\partial \Omega)}$ and
$\Vert f\Vert _{\scriptstyle L^{\bar{p}(\cdot)}(\Omega)}$ are the usual
Lebesgue norms with variable exponent.
