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Nonembedding of Lorentz sequence spaces into Lorentz function spaces
Abstract
Let 0<p, q<∞ with p ≠ q, and suppose that p<2 or q ≤ 1. We prove that the Lorentz sequence space ℓp, q does not isomorphically embed into Lp, q(0,1). Consequently, Lp, q(0, ∞) does not isomorphically embed into Lp, q(0,1).
Related
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BibTeX
@misc{qi2026nonembedding,
title = {{Nonembedding of Lorentz sequence spaces into Lorentz function spaces}},
author = {Junxiang Qi and Qi Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29512},
eprint = {2609.29512},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29512},
}
RIS
TY - UNPB
TI - Nonembedding of Lorentz sequence spaces into Lorentz function spaces
AU - Junxiang Qi
AU - Qi Liu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29512
UR - https://arxiv.org/abs/2609.29512
AB - Let 0<p, q<∞ with p ≠ q, and suppose that p<2 or q ≤ 1. We prove that the Lorentz sequence space ℓ_p, q does not isomorphically embed into L_p, q(0,1). Consequently, L_p, q(0, ∞) does not isomorphically embed into L_p, q(0,1).
ER -