Function spaces via fractional Poisson kernel on Carnot groups and applications. (English) Zbl 1539.43001
The methods in this paper give a new characterization of homogeneous Besov and Sobolev spaces in Carnot groups using the fractional heat kernel and Poisson kernel. Moreover, several applications to estimates for commutators of fractional powers of the sub-Laplacian are provided.
Though technically not difficult and the proofs may follow the classical results, these results are worthy to be written up in the literature for future reference.
Though technically not difficult and the proofs may follow the classical results, these results are worthy to be written up in the literature for future reference.
Reviewer: Jinsen Xiao (Guangzhou)
MSC:
| 43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
| 43A80 | Analysis on other specific Lie groups |
| 42B35 | Function spaces arising in harmonic analysis |
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