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We consider a family of measures on a q-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for that measures, and we prove interpolation results involving such spaces. As a consequence we have boundedness results for integral operators involving Hardy, BMO, and \(L^p\) spaces.

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H1 and BMO Spaces for Exponentially Decreasing Measures on Homogeneous Trees

  • 会议论文

  • 发表日期：

    2026年

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  • Matteo Monti

摘要

We consider a family of measures on a q-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for that measures, and we prove interpolation results involving such spaces. As a consequence we have boundedness results for integral operators involving Hardy, BMO, and \(L^p\) spaces.