In this paper we develop a theory of Besov and Triebel–Lizorkin spaces on general noncompact connected Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a measure whose density with respect to a right Haar measure is a continuous positive character of the group. We prove several equivalent characterizations of their norms, we establish comparison results also involving Sobolev spaces of recent introduction, and investigate their complex interpolation and algebra properties.

中文翻译：

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李群上的 Besov 和 Triebel-Lizorkin 空间

在本文中，我们在具有亚黎曼结构的一般非紧连通李群上开发了 Besov 和 Triebel-Lizorkin 空间理论。这些空间是通过具有漂移的亚椭圆亚拉普拉斯算子定义的，并赋予了一个测度，该测度相对于右 Haar 测度的密度是群的连续正特征。我们证明了它们的范数的几个等效特征，我们建立了也涉及最近引入的 Sobolev 空间的比较结果，并研究了它们的复杂插值和代数性质。