Spectral Multipliers for Hardy Spaces Associated with Schrodinger Operators with Polynomial Potentials

Let T_t be the semigroup of linear operators generated by a Schrödingeroperator – A = – V, where V is a non-negative polynomial,and let be the spectral resolution of A. We say that f is an element of if the maximal function Mf(x) = sup_t>0|T_tf(x)| belongs toL_p. We prove a criterion of Mihlin type on functions F whichimplies boundedness of the operators on , 0 < p 1. 1991 MathematicsSubject Classification 42B30, 35J10.