Year: 2025
Type: article
Abstract: This paper explores the interactions of absolute continuity of the (quasi)norm with the concepts that are fundamental in the theory of rearrangement-invariant (quasi-)Banach function spaces, such as the Luxemburg representation or the Hardy–Littlewood–Pólya relation. In order to prove our main results, we give an explicit construction of a particularly suitable representation quasinorm (which is not necessarily unique) and develop several new tools that we believe to be of independent interest. As an application of our results, we characterise the subspace of functions having absolutely continuous quasinorms in weak Marcinkiewicz spaces.
Source: Revista Matemática Complutense
Author: Dalimil Peša
Institutions: Charles University, Chemnitz University of Technology
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415148707