Spectral multipliers for Hardy spaces associated with Schrodinger operators with polynomial potentials

摘要

Let Tt be the semigroup of linear operators generated by a Schrodinger operator -A = Delta - V, where V is a non-negative polynomial, and let integral(0)(infinity) lambda dE(A)(lambda) be the spectral resolution of A. We say that f is an element of H-A(P) if the maximal function Mf(x) = sup(t>0) /Tt f(x)/ belongs to L-P. We prove a criterion of Mihlin type on functions F which implies boundedness of the operators F(A) = integral(0)(infinity) F(lambda) dE(A)(lambda) on H-A(P), 0 < p less than or equal to 1. [References: 19]