PreprintCC BY 4.0arXiv
On Certian Fine Properties of Sequence Spaces
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.
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BibTeX
@misc{kamenik2026certian,
title = {{On Certian Fine Properties of Sequence Spaces}},
author = {Hanuš Kameník},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17143},
eprint = {2609.17143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Certian Fine Properties of Sequence Spaces
AU - Hanuš Kameník
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17143
UR - https://arxiv.org/abs/2609.17143
AB - 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.
ER -