SPECTRAL MULTIPLIERS FOR HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS WITH POLYNOMIAL POTENTIALS
Published online by Cambridge University Press: 23 October 2000
Abstract
Let Tt be the semigroup of linear operators generated by a Schrödinger operator − A = Δ − V, where V is a non-negative polynomial, and let ∫∞0λdEA(λ) be the spectral resolution of A. We say that f is an element of HpA if the maximal function [Mscr ]f(x) = supt>0[mid ]Ttf(x)[mid ] belongs to Lp. We prove a criterion of Mihlin type on functions F which implies boundedness of the operators F(A) = ∫∞0F(λ)dEA(λ) on HpA, 0 < p [les ] 1.
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