Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
type: Item
instance of: scholarly article
title: Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
zbMATH Open document ID: 0664.46026
DOI: 10.1007/BF02384402
published in: Arkiv för Matematik
publication date: 1986-01-01T00:00:00Z
review text: The families of spaces \(B^ s_{pq}\) and \(F^ s_{pq}\) \((-\infty <s<\infty,0<p\leq \infty)\) were introduced by J. Peetre, P. I. Lizorkin, and the author. For a suitable choice of parameters these families include most of the known function spaces defined by differentiability and smoothness conditions. In the present article these spaces are defined on a complete Riemannian manifold that satisfies suitable uniformity conditions. The project requires a local definition of the spaces in question which is to be found in previous work of the author. It turns out that while there is a natural definition of the F spaces on a manifold, some technical difficulties arise in the case of B spaces; in the present paper these are defined by means of real interpolation. Various results about spaces on manifolds are established, in particular, inclusions and isomorphisms by means of Bessel kernels and interpolation properties. Forthcoming papers on the subject are announced.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 58D15
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 4086300
zbMATH Keywords: differentiability and smoothness conditions
zbMATH Keywords: complete Riemannian manifold
zbMATH Keywords: uniformity conditions
zbMATH Keywords: real interpolation
zbMATH Keywords: Bessel kernels
author: Hans Triebel
MaRDI profile type: Publication
Wikidata QID: Q115392361
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description: scientific article; zbMATH DE number 4086300