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October 2010 Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials
Jacek Dziubański, Marcin Preisner
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Ark. Mat. 48(2): 301-310 (October 2010). DOI: 10.1007/s11512-010-0121-5

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 RjfL1(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

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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

Information

Received: 19 February 2009; Revised: 20 January 2010; Published: October 2010
First available in Project Euclid: 31 January 2017

zbMATH: 1202.42046
MathSciNet: MR2672611
Digital Object Identifier: 10.1007/s11512-010-0121-5

Rights: 2010 © Institut Mittag-Leffler

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Vol.48 • No. 2 • October 2010
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