, Volume 184, Issue 3, pp 315-326

Hardy spaces H 1 for Schrödinger operators with compactly supported potentials

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Abstract

Let L=-Δ+V be a Schrödinger operator on ℝ d , d≥3, where V is a non-negative compactly supported potential that belongs to L p for some p>d/2. Let {K t } t>0 denote the semigroup of linear operators generated by -L. For a function f we define its H 1 L -norm by $\| f\|_{H^1_L}=\| \sup_{t>0} |K_t f(x)|\|_{L^1(dx)}$ . It is proved that for a properly defined weight w a function f belongs to H 1 L if and only if wfH 1(ℝ d ), where H 1(ℝ d ) is the classical real Hardy space.

Mathematics Subject Classification (2000)

42B30, 35J10, 42B25