Averaging operators on decreasing or positive functions: Equivalence and optimal bounds
We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S∗, on the full range 1 ≤ p ≤ ∞, for the cases of decreasing, positive or general functions (in fact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/93658 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/93658 |
| Access Level: | acceso abierto |
| Palabra clave: | Hardy operator Dual operator Bests constants Decreasing functions Ciencias 12 Matemáticas |
| Sumario: | We study the optimal bounds for the Hardy operator S minus the identity, as well as S and its dual operator S∗, on the full range 1 ≤ p ≤ ∞, for the cases of decreasing, positive or general functions (in fact, these two kinds of inequalities are equivalent for the appropriate cone of functions). For 1 < p ≤ 2, we prove that all these estimates are the same, but for 2 < p < ∞, they exhibit a completely different behavior. |
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