Besov spaces and Sobolev spaces on a nilpotent Lie group

Sobolev spaces on graded Lie groups

“…It is quite natural to try and generalise these spaces to a non-Euclidean setting, for instance on Lie groups. The development of analysis on nilpotent Lie groups was initiated by G. Folland and E. Stein in [13], and G. Folland was the first to define and study Sobolev spaces on stratified (nilpotent Lie) groups [12], see also [23]. Using Littlewood-Paley decompositions as well as heat kernel estimates for sub-Laplacians [1,25], this was generalised to Besov space on Lie groups of polynomial growth, see e.g.…”

Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières

“…Alors il existe une constante C positive ou nulle, telle que pour toute fonction (pe^R") portée par la boule \x\ ^ 1, pour tous XQ^R" et u > 0, on ait : (8) l|T((p^)IL < C(||(p||^ + ||(p|L + llq/IU. C'est un espace de distributions module les polynômes; cet espace ne dépend pas du choix de (p.…”

Approximation and Besov Spaces on Stratified Groups

“…For our purpose it is worthwhile to provide a different definition of Besov spaces. However a comparison between Theorems 12 of [10] and Proposition 4 below reveals that the spaces A (a, p, q) defined by Saka coincide with our spaces Bp . We recall that the case of the Lipschitz spaces (q = oo) in stratified groups have been studied in great detail by S. G. Krantz in [7] (see also [3]).…”

“…4. Besov spaces in stratified groups were widely studied by K. Saka in [10]. Following Stein's approach, Saka defines these spaces by using the heat semigroup.…”