Notes on compactness in Lp-spaces on locally compact groups
Krukowski, Mateusz (Lódz University of Technology (Lodz, Polònia). Institute of Mathematics)

Date:	2023
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Arzelà-ascoli theorem ; Kolmogorov-riesz theorem ; Weil theorem ; Sudakov theorem ; Young's convolution inequality
Published in:	Publicacions matemàtiques, Vol. 67 Núm. 2 (2023) , p. 687-713 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/418421
DOI: 10.5565/PUBLMAT6722308

27 p, 415.7 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles