Power-aggregation of pseudometrics and the McShane-Whitney extension theorem for Lipschitz p-convace maps
[EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggre...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/166134 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/166134 |
| Access Level: | acceso abierto |
| Palabra clave: | Pseudometric Aggregation Lipschitz function Extension P-average MATEMATICA APLICADA |
| Sumario: | [EN] Given a countable set of families {Dk:k¿N} of pseudometrics over the same set D, we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of ¿kDk. We prove that a Lipschitz function f is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of ¿kDk is fulfilled by f. In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a p-power domination, we say that the elements of Dk are p-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz p-concave real valued maps. |
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