  We show that characteristic functions of domains with boundaries transversal
to stable cones are bounded multipliers on a recently introduced scale
$U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0
and -(r-1)+t<s, with 1<p<infty. (Amended after comments from the referee and M.
J\'ez\'equel, January 10, 2018)
