1. Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups.
- Author
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Cardona, Duván and Ruzhansky, Michael
- Subjects
- *
BESOV spaces , *PSEUDODIFFERENTIAL operators , *COMPACT groups , *SOBOLEV spaces , *COMPACT spaces (Topology) , *ELLIPTIC operators , *LIE groups - Abstract
In this paper, we investigate the Besov spaces on compact Lie groups in a subelliptic setting, that is, associated with a family of vector fields, satisfying the Hörmander condition, and their corresponding sub-Laplacian. Embedding properties between subelliptic Besov spaces and Besov spaces associated to the Laplacian on the group are proved. We link the description of subelliptic Sobolev spaces with the matrix-valued quantisation procedure of pseudo-differential operators to provide sharp subelliptic Sobolev and Besov estimates for operators in the $ (\rho,\delta) $ (ρ , δ) -Hörmander classes. In contrast with the available results in the literature in the setting of compact Lie groups, we allow Fefferman-type estimates in the critical case $ \rho =\delta. $ ρ = δ. Interpolation properties between Besov spaces and Triebel–Lizorkin spaces are also investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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