Variable Bounded Variation Spaces in the Riesz sense
In this thesis we introduce the variable exponent bounded variation spaces in the Riesz sense, we prove some embedding results and show that a type of Riesz representation lemma is valid in the newly introduced spaces. On the other hand, we characterize global Lipschitz Nemytskii operators defined i...
- Autores:
-
Guzmán Fonseca, Oscar Mauricio
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2018
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/69130
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/69130
http://bdigital.unal.edu.co/70642/
- Palabra clave:
- 51 Matemáticas / Mathematics
Bounded variation
Variable exponent space
Nemitskii operator
Riesz representation lemma
Modular space
Variable exponent Bochner-Lebesgue spaces
Variación acotada
Espacio de exponente variable
Operador de Nemitskii
Lemma de representación de Riesz
Espacio modular
Espacio de Bochner-Lebesgue con exponente variable
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In this thesis we introduce the variable exponent bounded variation spaces in the Riesz sense, we prove some embedding results and show that a type of Riesz representation lemma is valid in the newly introduced spaces. On the other hand, we characterize global Lipschitz Nemytskii operators defined in the Riesz bounded variation space with variable exponent. Finally we characterize the linear functionals on variable exponent Bochner-Lebesgue spaces in terms of the variable exponent Riesz bounded variation spaces for vector measures. |
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