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Boundedness of pseudo-differential operators in subelliptic Sobolev and Besov spaces on compact Lie groups.
- Source :
-
Complex Variables & Elliptic Equations . Jul2024, Vol. 69 Issue 7, p1049-1082. 34p. - Publication Year :
- 2024
-
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]
Details
- Language :
- English
- ISSN :
- 17476933
- Volume :
- 69
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Complex Variables & Elliptic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 178176949
- Full Text :
- https://doi.org/10.1080/17476933.2023.2196416