  We consider fractional Sobolev spaces $H^\theta(\Gamma)$, $\theta \in [0,1]$,
on a 2D surface $\Gamma$. We show that functions in $H^\theta(\Gamma)$ can be
decomposed into contributions with local support in a stable way. Stability of
the decomposition is inherited by piecewise polynomial subspaces. Applications
include the analysis of additive Schwarz preconditioners for discretizations of
the hypersingular integral operator by the $p$-version of the boundary element
method with condition number bounds that are uniform in the polynomial degree
$p$.
