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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Detalhes bibliográficos
Autor: Chaparro Gutiérrez, Héctor Camilo
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
Descrição
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.