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Sharp Logarithmic Bounds for Vilenkin-Fejér Kernels
Abstract
Let Gm be a bounded Vilenkin group and put R:=supj mj. We prove the sharp uniform estimate |Kn|1≤ 17/(15ln 2)ln R, n≥1, for the Fejér kernels associated with the Vilenkin system. The constant 17/(15ln2) is best possible. In the Walsh--Paley case R=2, the result reduces exactly to Toledo's sharp estimate supn|Kn|1=17/15.
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BibTeX
@misc{areshidze2026sharp,
title = {{Sharp Logarithmic Bounds for Vilenkin-Fejér Kernels}},
author = {Nika Areshidze and George Tephnadze},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.09929},
eprint = {2611.09929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.09929},
}
RIS
TY - UNPB
TI - Sharp Logarithmic Bounds for Vilenkin-Fejér Kernels
AU - Nika Areshidze
AU - George Tephnadze
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.09929
UR - https://arxiv.org/abs/2611.09929
AB - Let G_m be a bounded Vilenkin group and put R:=sup_j m_j. We prove the sharp uniform estimate |K_n|_1≤ 17/(15ln 2)ln R, n≥1, for the Fejér kernels associated with the Vilenkin system. The constant 17/(15ln2) is best possible. In the Walsh--Paley case R=2, the result reduces exactly to Toledo's sharp estimate sup_n|K_n|_1=17/15.
ER -