Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
In this thesis we study the multidimensional Lorentz spaces via the two-dimensional decreasing rearrangement. In particular, results of interpolation, quasinormability and completeness are stablished, and weights that define a norm are characterized. The boundedness, compactness and closed range of...
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| Formato: | tesis doctoral |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | Colombia |
| Recursos: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/64024 |
| Acesso em linha: | https://repositorio.unal.edu.co/handle/unal/64024 http://bdigital.unal.edu.co/64726/ |
| Access Level: | acceso abierto |
| Palavra-chave: | 5 Ciencias naturales y matemáticas / Science 51 Matemáticas / Mathematics Decreasing rearrangement Composition operator Multipliers Multidimensional rearrangement Lorentz spaces Reordenamiento decreciente Reordenamiento multidimensional Multiplicadores Operador compacto Espacios de Lorentz |
| Resumo: | In this thesis we study the multidimensional Lorentz spaces via the two-dimensional decreasing rearrangement. In particular, results of interpolation, quasinormability and completeness are stablished, and weights that define a norm are characterized. The boundedness, compactness and closed range of the weighted composition operator defined on those spaces are also characterized. Finally, we present the Bounded $p$-variation spaces in the Wiener's sense, and then we characterize the set of multipliers between them. |
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