Abstract
Let {K t } t>0 be the semigroup of linear operators generated by a Schrödinger operator −L = Δ − V (x) on ℝd, d ≥ 3, where V (x) ≥ 0 satisfies Δ −1 V ∈ L ∞. We say that an L 1-function f belongs to the Hardy space \({H^{1}_{L}}\) if the maximal function ℳ L f (x) = sup t>0 |K t f (x)| belongs to L 1 (ℝd). We prove that the operator (−Δ)1/2 L −1/2 is an isomorphism of the space \({H^{1}_{L}}\) with the classical Hardy space H 1(ℝd) whose inverse is L 1/2(−Δ)−1/2. As a corollary we obtain that the space \({H^{1}_{L}}\) is characterized by the Riesz transforms \(R_{j}=\frac {\partial }{\partial x_{j}}L^{-1\slash 2}\).
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The research was supported by Polish funds for sciences, grants: DEC-2012/05/B/ST1/00672 and DEC-2012/05/B/ST1/00692 from Narodowe Centrum Nauki.
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Dziubański, J., Zienkiewicz, J. A Characterization of Hardy Spaces Associated with Certain Schrödinger Operators. Potential Anal 41, 917–930 (2014). https://doi.org/10.1007/s11118-014-9400-2
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DOI: https://doi.org/10.1007/s11118-014-9400-2