Peer-reviewedCC BY 4.0Mathematics
Hyperbolic Lebesgue Constants in Dimension Three
- 1Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
Abstract
For the three-dimensional hyperbolic crosses {k∈Z3,α,β,γ>0:1≤|k1|α|k2|β|k3|γ≤Rα+β+γ}, three types of estimates (from above) of the Lebesgue constants generated by them are possible depending on α, β, and γ. We improve the most problematic of them by showing that for R→∞, it may be RlnR rather than the previously known RlnR.
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BibTeX
@article{liflyand2026hyperbolic,
title = {{Hyperbolic Lebesgue Constants in Dimension Three}},
author = {Elijah Liflyand},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214069},
url = {https://www.mdpi.com/2227-7390/14/21/4069},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Hyperbolic Lebesgue Constants in Dimension Three
AU - Elijah Liflyand
PY - 2026
DA - 2026/11/06
JO - Mathematics
DO - 10.3390/math14214069
UR - https://www.mdpi.com/2227-7390/14/21/4069
AB - For the three-dimensional hyperbolic crosses {k∈Z3,α,β,γ>0:1≤|k1|α|k2|β|k3|γ≤Rα+β+γ}, three types of estimates (from above) of the Lebesgue constants generated by them are possible depending on α, β, and γ. We improve the most problematic of them by showing that for R→∞, it may be RlnR rather than the previously known RlnR.
SN - 2227-7390
ER -