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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]

The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential J m , A and corresponding L p -Sobolev space. Moreover, the Schwartz-type space S A is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The L p -boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces H A m , p and H A m , p are given. [ABSTRACT FROM AUTHOR]