  We provide an endpoint stability result for Scott-Zhang type operators in
Besov spaces. For globally continuous piecewise polynomials these are bounded
from $H^{3/2}$ into $B^{3/2}_{2,\infty}$; for elementwise polynomials these are
bounded from $H^{1/2}$ into $B^{1/2}_{2,\infty}$. As an application, we obtain
a multilevel decomposition based on Scott-Zhang operators on a hierarchy of
meshes generated by newest vertex bisection with equivalent norms up to (but
excluding) the endpoint case. A local multilevel diagonal preconditioner for
the fractional Laplacian on locally refined meshes with optimal eigenvalue
bounds is presented.
