Interpolation of Sobolev spaces, Littlewood-Paley inequalities and Riesz transforms on graphs
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 < +∞. T...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:49669 |
| Acceso en línea: | https://ddd.uab.cat/record/49669 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_53209_02 |
| Access Level: | acceso abierto |
| Palabra clave: | Graphs Discrete Laplacian Riesz transforms Littlewood-Paley inequalities Sobolev spaces Interpolation |
| Sumario: | 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. |
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