Rearrangement-invariant norms commuting with dilations
We study rearrangement-invariant spaces X over [0, ∞) for which there exists a function h : (0, ∞) → (0, ∞) such that ∥Drf∥X = h(r)∥f∥X for all f ∈ X and all r > 0, where Dr is the dilation operator. It is shown that this may hold only if h(r) = r− 1 p for all r > 0, in which case the norm ∥·∥...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/131938 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/131938 |
| Access Level: | acceso abierto |
| Palabra clave: | Rearrangement-invariant spaces Dilation Homogeneity Orlicz–Lorentz spaces Ciencias 12 Matemáticas 1202 Análisis y Análisis Funcional |
| Sumario: | We study rearrangement-invariant spaces X over [0, ∞) for which there exists a function h : (0, ∞) → (0, ∞) such that ∥Drf∥X = h(r)∥f∥X for all f ∈ X and all r > 0, where Dr is the dilation operator. It is shown that this may hold only if h(r) = r− 1 p for all r > 0, in which case the norm ∥·∥X is called p-homogeneous. We investigate which types of r.i. spaces satisfy this condition and show some important embedding properties. |
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