Notes on compactness in Lp-spaces on locally compact groups

Main Article Content

Mateusz Krukowski

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.

Paraules clau
Arzelà–Ascoli theorem, Kolmogorov–Riesz theorem, Weil theorem, Sudakov theorem, Young’s convolution inequality

Article Details

Com citar
Krukowski, Mateusz. «Notes on compactness in Lp-spaces on locally compact groups». Publicacions Matemàtiques, 2023, vol.VOL 67, núm. 2, p. 687–713, https://raco.cat/index.php/PublicacionsMatematiques/article/view/418421.
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