Characteristic functions as bounded multipliers on anisotropic spaces

We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U_p^{t,s}$ 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)