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.
Besov and Triebel–Lizorkin spaces on Lie groups / T. Bruno, M.M. Peloso, M. Vallarino. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 377:1-2(2020 Jun), pp. 355-377. [10.1007/s00208-019-01927-z]
Besov and Triebel–Lizorkin spaces on Lie groups
M.M. Peloso
Secondo
;
2020
Abstract
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.File | Dimensione | Formato | |
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