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Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs
Badr, Nadine (Université Claude Bernard Lyon I)
Russ, Emmanuel (Université Paul Cézanne. Faculté des Sciences et Techniques de Saint-Jérôme)

Data: 2009
Resum: Let Γ be a graph endowed with a reversible Markov kernel p, and P the associated operator, defined by Pf(x) = P y p(x, y)f(y). Denote by ∇ the discrete gradient. We give necessary and/or sufficient conditions on Γ in order to compare k∇fkp and‚ ‚(I − P) 1/2f‚ p uniformly in f for 1 < p < +∞. These conditions are different for p < 2 and p > 2. The proofs rely on recent techniques developed to handle operators beyond the class of Calderón-Zygmund operators. For our purpose, we also prove Littlewood-Paley inequalities and interpolation results for Sobolev spaces in this context, which are of independent interest.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Graphs ; Discrete Laplacian ; Riesz transforms ; Littlewood-Paley inequalities ; Sobolev spaces ; Interpolation
Publicat a: Publicacions Matemàtiques, V. 53 n. 2 (2009) p. 273-328, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_53209_02

56 p, 390.1 KB

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