Abstract
Let L=−Δ+V be a Schrödinger operator on ℝd, d≥3. We assume that V is a nonnegative, compactly supported potential that belongs to Lp(ℝd), for some p> d/2. Let Kt be the semigroup generated by −L. We say that an L1(ℝd)-function f belongs to the Hardy space $H^{1}_{L}$ associated with L if sup t>0|Ktf| belongs to L1(ℝd). We prove that $f\in H^{1}_{L}$ if and only if Rjf∈L1(ℝd) for j=1,…, d, where Rj=(∂/∂xj)L−1/2 are the Riesz transforms associated with L.
Funding Statement
Supported by the Polish Ministry of Science and High Education—grant N N201 397137, the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic Analysis, Nonlinear Analysis and Probability" MTKD-CT-2004-013389.
Citation
Jacek Dziubański. Marcin Preisner. "Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials." Ark. Mat. 48 (2) 301 - 310, October 2010. https://doi.org/10.1007/s11512-010-0121-5
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