Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

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Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

Bui, The Anh; Hong, Qing; Hu, Guorong

Journal of functional analysis, 05/2024, Volume: 286, Issue: 10

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Let L=−ΔHn+μ be a generalized Schrödinger operator on the Heisenberg group Hn, where ΔHn is the sub-Laplacian, and μ is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of L. Applying these estimates, we then study the Hardy spaces HL1(Hn) introduced in terms of the maximal function associated with the heat semigroup e−tL; in particular, we obtain an atomic decomposition of HL1(Hn), and prove the Riesz transform characterization of HL1(Hn). The dual space of HL1(Hn) is also studied.

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