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Hardy-Hausdorff spaces on the Heisenberg group

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Abstract

In this paper, by using the tent spaces on the Siegel upper half space, which are defined in terms of Choquet integrals with respect to Hausdorff capacity on the Heisenberg group, the Hardy-Hausdorff spaces on the Heisenberg group are introduced. Then, by applying the properties of the tent spaces on the Siegel upper half space and the Sobolev type spaces on the Heisenberg group, the atomic decomposition of the Hardy-Hausdorff spaces is obtained. Finally, we prove that the predual spaces of Q spaces on the Heisenberg group are the Hardy-Hausdorff spaces.

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  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, China

    Kai Zhao

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Zhao, K. Hardy-Hausdorff spaces on the Heisenberg group. Sci. China Math. 59, 2167–2184 (2016). https://doi.org/10.1007/s11425-016-0062-9

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  • DOI: https://doi.org/10.1007/s11425-016-0062-9

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