Endpoint boundedness of toroidal pseudo-differential operators

In this note, we prove that the toroidal pseudo-differential operator is bounded from L-infinity(T-n)to BMO(Tn) if the symbol belongs to the toroidal Hormander class Sn(rho-1)/2 rho,delta(TnxZn)S rho, with 0<rho <= 1 and 0 <=delta<1 . As a corollary, we obtain a result of toroidal pseudo-differential operators on L-p when 2<p<infinity 2<p<infinity for symbols in the class S(rho,delta)(m)m(T(n)xZ(n)) with m <= n(rho-1)(1/2-1/p)+npmin{0,rho-delta} .