In this paper we discuss function spaces on a general noncompact Lie group, namely the scales of Triebel–Lizorkin and Besov spaces, defined in terms of a sub-Laplacian with drift. The sub-Laplacian is written as the (negative) sum of squares of a collection of left-invariant vector fields satisfying Hörmander’s condition. These spaces were recently introduced by the authors. In this paper we prove a norm characterization in terms of finite differences, the density of test functions, and related isomorphism properties.
CITATION STYLE
Bruno, T., Peloso, M. M., & Vallarino, M. (2021). Potential Spaces on Lie Groups. In Springer INdAM Series (Vol. 45, pp. 149–192). Springer-Verlag Italia s.r.l. https://doi.org/10.1007/978-3-030-72058-2_4
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