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 -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
Interpolation properties between Besov spaces and Triebel–Lizorkin spaces are also investigated.
AMS SUBJECT CLASSIFICATIONS:
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 A is defined by
is the Fourier transform of f, and σ satisfies the
-conditions
2 A is defined by
is the Fourier transform of f, and σ satisfies the
-conditions