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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Autores:
Chaparro Gutiérrez, Héctor Camilo
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/64024
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/64024
http://bdigital.unal.edu.co/64726/
Palabra clave:
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
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Castillo, René ErlínChaparro Gutiérrez, Héctor Camiloc1f18fd6-15b6-449f-8628-53e40de8f4e63002019-07-02T22:24:24Z2019-07-02T22:24:24Z2018-04-25https://repositorio.unal.edu.co/handle/unal/64024http://bdigital.unal.edu.co/64726/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.Resumen: En esta tesis se estudian los espacios de Lorentz multidimensionales via el reordenamiento decreciente bidimensional. En particular, se establecen resultados de interpolación, cuasinormabilidad y completitud, y se caracterizan los pesos que definen una norma. La acotación, compacidad y rango cerrado del operador composición con peso definido en esos espacios también son caracterizados. Finalmente, se presentan los espacios de p-variación acotada, y se caracteriza el conjunto de multiplicadores entre ellos.Doctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de MatemáticasDepartamento de MatemáticasChaparro Gutiérrez, Héctor Camilo (2018) Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.5 Ciencias naturales y matemáticas / Science51 Matemáticas / MathematicsDecreasing rearrangementComposition operatorMultipliersMultidimensional rearrangementLorentz spacesReordenamiento decrecienteReordenamiento multidimensionalMultiplicadoresOperador compactoEspacios de LorentzWeighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spacesTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDORIGINALPhD_Thesis_Camilo_Chaparro.pdfapplication/pdf7634771https://repositorio.unal.edu.co/bitstream/unal/64024/1/PhD_Thesis_Camilo_Chaparro.pdf1cef6391ada383a20707a18d165ce01eMD51THUMBNAILPhD_Thesis_Camilo_Chaparro.pdf.jpgPhD_Thesis_Camilo_Chaparro.pdf.jpgGenerated Thumbnailimage/jpeg4890https://repositorio.unal.edu.co/bitstream/unal/64024/2/PhD_Thesis_Camilo_Chaparro.pdf.jpg954e5f8121a1d67860e87103c8a4be07MD52unal/64024oai:repositorio.unal.edu.co:unal/640242024-05-02 23:24:11.879Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
title Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
spellingShingle Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
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
title_short Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
title_full Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
title_fullStr Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
title_full_unstemmed Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
title_sort Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces
dc.creator.fl_str_mv Chaparro Gutiérrez, Héctor Camilo
dc.contributor.author.spa.fl_str_mv Chaparro Gutiérrez, Héctor Camilo
dc.contributor.spa.fl_str_mv Castillo, René Erlín
dc.subject.ddc.spa.fl_str_mv 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
topic 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
dc.subject.proposal.spa.fl_str_mv Decreasing rearrangement
Composition operator
Multipliers
Multidimensional rearrangement
Lorentz spaces
Reordenamiento decreciente
Reordenamiento multidimensional
Multiplicadores
Operador compacto
Espacios de Lorentz
description 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.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-04-25
dc.date.accessioned.spa.fl_str_mv 2019-07-02T22:24:24Z
dc.date.available.spa.fl_str_mv 2019-07-02T22:24:24Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/64024
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/64726/
url https://repositorio.unal.edu.co/handle/unal/64024
http://bdigital.unal.edu.co/64726/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas
Departamento de Matemáticas
dc.relation.references.spa.fl_str_mv Chaparro Gutiérrez, Héctor Camilo (2018) Weighted composition operators on multidimensional Lorentz spaces and a glimpse on multipliers between bounded p-variation spaces. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/64024/1/PhD_Thesis_Camilo_Chaparro.pdf
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repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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