Revista Matemática Complutense

, Volume 24, Issue 1, pp 251–275 | Cite as

Maximal function characterizations of Hardy spaces associated with Schrödinger operators on nilpotent Lie groups

Article

Abstract

Let G be a connected and simply connected nilpotent Lie group and L≡−Δ+W be the Schrödinger operator on L 2(G), where \(0\le W\in L^{1}_{\mathrm{loc}}(G)\). In this paper, the authors establish some equivalent characterizations of the Hardy space \(H^{p}_{L}(G)\) for p∈(0,1] in terms of the radial maximal functions and non-tangential maximal functions associated with \(\{e^{-t^{2}L}\}_{t>0}\) and \(\{e^{-t\sqrt{L}}\}_{t>0}\), respectively. The boundedness of the Riesz transform \(\nabla L^{-\frac{1}{2}}\) from \(H^{p}_{L}(G)\) to L p (G) with p∈(0,1] and from \(H^{p}_{L}(G)\) to H p (G) with p∈(D/(D+1),1] are also obtained, where D is the dimension at infinity of G.

Keywords

Nilpotent Lie group Hardy space Schrödinger operator Maximal function Riesz transform 

Mathematics Subject Classification (2000)

42B25 42B20 42B30 22E25 43A15 

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© Revista Matemática Complutense 2010

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex SystemsMinistry of EducationBeijingPeople’s Republic of China

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