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<p>In this paper, we are devoted to proving the Bourgain–Brezis–Mironescu formula on the Heisenberg group and investigating the connection between the BV space and the fractional Sobolev space. Moreover, the Bourgain–Brezis–Mironescu formula on the Carnot group can also be derived using a similar method that parallels the approach used for the Heisenberg group.</p>

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The Bourgain–Brezis–Mironescu formula on the Heisenberg group

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Xiangyun Xie,
  • Pengtao Li,
  • Yu Liu

摘要

In this paper, we are devoted to proving the Bourgain–Brezis–Mironescu formula on the Heisenberg group and investigating the connection between the BV space and the fractional Sobolev space. Moreover, the Bourgain–Brezis–Mironescu formula on the Carnot group can also be derived using a similar method that parallels the approach used for the Heisenberg group.