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

Author： Jiang Renjin  

Publisher： Springer Publishing Company

ISSN： 1139-1138

Source： Revista Matem??tica Complutense, Vol.24, Iss.1, 2011-01, pp. : 251-275

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Abstract

Let G be a connected and simply connected nilpotent Lie group and L≡−Δ+W be the Schrödinger operator on L2(G), where $0le Win L^{1}_{mathrm{loc}}(G)$ . 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 ${e^{-tsqrt{L}}}_{t>0}$ , respectively. The boundedness of the Riesz transform $abla L^{-frac{1}{2}}$ from $H^{p}_{L}(G)$ to Lp(G) with p∈(0,1] and from $H^{p}_{L}(G)$ to Hp(G) with p∈(D/(D+1),1] are also obtained, where D is the dimension at infinity of G.

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