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.
Potential Spaces on Lie Groups / T. Bruno, M.M. Peloso, M. Vallarino (SPRINGER INDAM SERIES). - In: Geometric Aspects of Harmonic Analysis / [a cura di] P. Ciatti, A. Martini. - [s.l] : Springer-Verlag, 2021. - ISBN 978-3-030-72057-5. - pp. 149-192 (( convegno Geometric Aspects of Harmonic Analysis tenutosi a Cortona nel 2018 [10.1007/978-3-030-72058-2_4].
Potential Spaces on Lie Groups
M.M. Peloso
Secondo
;
2021
Abstract
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.
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