Lorentz-Shimogaki and Boyd Theorems for weighted Lorentz spaces
We prove the Lorentz-Shimogaki and Boyd theorems for the spaces Λpu(w). As a consequence, we give the complete characterization of the strong boundedness of H on these spaces in terms of some geometric conditions on the weights u and w, whenever p > 1. For these values of p, we also give the comp...
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| Autores principales: | , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2014
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/101707 https://ri.conicet.gov.ar/11336/12164 https://academic.oup.com/jlms/article-abstract/89/2/321/833025/Lorentz-Shimogaki-and-Boyd-theorems-for-weighted?redirectedFrom=fulltext |
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| Sumario: | We prove the Lorentz-Shimogaki and Boyd theorems for the spaces Λpu(w). As a consequence, we give the complete characterization of the strong boundedness of H on these spaces in terms of some geometric conditions on the weights u and w, whenever p > 1. For these values of p, we also give the complete solution of the weak-type boundedness of the Hardy Littlewood operator on Λpu(w). |
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