Notes on compactness in Lp-spaces on locally compact groups

The main goal of the paper is to provide new insight into compactness in Lp-spaces on locally compact groups. The article begins with a brief historical overview and the current state of literature regarding the topic. Subsequently, we "take a step back" and investigate the Arzel'a-As...

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Detalles Bibliográficos
Autor: Krukowski, Mateusz|||0000-0001-6644-5633
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:280953
Acceso en línea:https://ddd.uab.cat/record/280953
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722308
Access Level:acceso abierto
Palabra clave:Arzelà-ascoli theorem
Kolmogorov-riesz theorem
Weil theorem
Sudakov theorem
Young's convolution inequality
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spelling Notes on compactness in Lp-spaces on locally compact groupsKrukowski, Mateusz|||0000-0001-6644-5633Arzelà-ascoli theoremKolmogorov-riesz theoremWeil theoremSudakov theoremYoung's convolution inequalityThe main goal of the paper is to provide new insight into compactness in Lp-spaces on locally compact groups. The article begins with a brief historical overview and the current state of literature regarding the topic. Subsequently, we "take a step back" and investigate the Arzel'a-Ascoli theorem on a non-compact domain together with one-point compactification. The main idea comes in Section 3, where we introduce the "Lp-properties" (Lp-boundedness, Lp-equicontinuity, and Lp-equivanishing) and study their "behaviour under convolution". The paper proceeds with an analysis of Young's convolution inequality, which plays a vital role in the final section. During the "grand finale", all the pieces of the puzzle are brought together as we lay down a new approach to compactness in Lp-spaces on locally compact groups. 22023-01-0120232023-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/280953https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722308reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2809532026-06-06T12:50:31Z
dc.title.none.fl_str_mv Notes on compactness in Lp-spaces on locally compact groups
title Notes on compactness in Lp-spaces on locally compact groups
spellingShingle Notes on compactness in Lp-spaces on locally compact groups
Krukowski, Mateusz|||0000-0001-6644-5633
Arzelà-ascoli theorem
Kolmogorov-riesz theorem
Weil theorem
Sudakov theorem
Young's convolution inequality
title_short Notes on compactness in Lp-spaces on locally compact groups
title_full Notes on compactness in Lp-spaces on locally compact groups
title_fullStr Notes on compactness in Lp-spaces on locally compact groups
title_full_unstemmed Notes on compactness in Lp-spaces on locally compact groups
title_sort Notes on compactness in Lp-spaces on locally compact groups
dc.creator.none.fl_str_mv Krukowski, Mateusz|||0000-0001-6644-5633
author Krukowski, Mateusz|||0000-0001-6644-5633
author_facet Krukowski, Mateusz|||0000-0001-6644-5633
author_role author
dc.subject.none.fl_str_mv Arzelà-ascoli theorem
Kolmogorov-riesz theorem
Weil theorem
Sudakov theorem
Young's convolution inequality
topic Arzelà-ascoli theorem
Kolmogorov-riesz theorem
Weil theorem
Sudakov theorem
Young's convolution inequality
description The main goal of the paper is to provide new insight into compactness in Lp-spaces on locally compact groups. The article begins with a brief historical overview and the current state of literature regarding the topic. Subsequently, we "take a step back" and investigate the Arzel'a-Ascoli theorem on a non-compact domain together with one-point compactification. The main idea comes in Section 3, where we introduce the "Lp-properties" (Lp-boundedness, Lp-equicontinuity, and Lp-equivanishing) and study their "behaviour under convolution". The paper proceeds with an analysis of Young's convolution inequality, which plays a vital role in the final section. During the "grand finale", all the pieces of the puzzle are brought together as we lay down a new approach to compactness in Lp-spaces on locally compact groups.
publishDate 2023
dc.date.none.fl_str_mv 2
2023-01-01
2023
2023-01-01
dc.type.none.fl_str_mv Article
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url https://ddd.uab.cat/record/280953
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6722308
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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