Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces
By Amiran Gogatishvili, Pekka Koskela, Yuan Zhou. 2011
94 citations recorded by the source corpus.
Abstract. On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel–Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a Poincaré inequality.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/2e1ecc92e1fdcaaa27a1788806e0ff47b46b431e
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In Applied Mathematics
- Dachun Yang
- Yuan Zhou
- Liguang Liu
- Diego Maldonado
- L. Ihnatsyeva
- T. Heikkinen
- Loukas Grafakos
- Heli Tuominen
Citations in the corpus
- Measure Density and Extension of Besov and Triebel–Lizorkin Functions (2014, background): “Following [9] and [11], we define a modulus of smoothness which does not rely on the group structure of the underlying space and which, for a function u ∈ L(R), is comparable with ω(u, t)p.”
- Fractional Sobolev extension and imbedding (2014, background): “The second conclusion (2.6) was essentially proved in [10, (2.4)] (see also [20, (5.9)]).”
- Multilinear analysis on metric spaces (2014, background): “RD-spaces have become the underlying context in numerous areas of analysis and PDEs, we refer the reader to [22, 23], [60, 61, 86], [71, 72, 40], [107, 109, 108] and references therein.”