Year: 2026
Type: preprint
Abstract: We develop a theory of Orlicz and Lorentz--Zygmund sequence spaces. We study in detail elementary properties of both structures. In particular, we characterize the values of governing parameters for which the corresponding spaces satisfy the axioms of rearrangement-invariant Banach sequence spaces, we evaluate the asymptotic behavior of their fundamental functions, and we characterize their associate spaces. In our main result, we characterize all cases in which a Lorentz--Zygmund sequence space coincides with some Orlicz sequence space.
Source: arXiv (Cornell University)
Author: Kameník, Hanuš
Institution: Charles University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213421995