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Heat and harmonic extensions for function spaces of Hardy-Sobolev-Besov type on symmetric spaces and Lie groups. (English) Zbl 0918.43007

Spaces of Hardy-Sobolev-Besov type \(B^s_{pq}\) and \(F^s_{pq}\) on (special) Riemannian manifolds and Lie groups are usually introduced via local charts. It is the aim of this paper to characterize these spaces intrinsically via heat and Poisson semigroups. Atomic decompositions of these spaces are the main tool.
Reviewer: H.Triebel (Jena)

MSC:

43A85 Harmonic analysis on homogeneous spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
22E30 Analysis on real and complex Lie groups
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