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Two-sided logarithmic estimates of the Lebesgue constants with respect to Vilenkin systems
Abstract
We introduce a new logarithmic digit variation for Vilenkin--Fourier partial sums and establish two-sided estimates for the corresponding Lebesgue constants with universal constants. These estimates hold for both bounded and unbounded Vilenkin systems. As an application, we show that bounded logarithmic variation yields uniform boundedness of the corresponding partial-sum operators on L1, L1-norm convergence for every integrable function, and almost everywhere convergence.
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BibTeX
@misc{tephnadze2026twosided,
title = {{Two-sided logarithmic estimates of the Lebesgue constants with respect to Vilenkin systems}},
author = {George Tephnadze},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35900},
eprint = {2610.35900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35900},
}
RIS
TY - UNPB
TI - Two-sided logarithmic estimates of the Lebesgue constants with respect to Vilenkin systems
AU - George Tephnadze
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35900
UR - https://arxiv.org/abs/2610.35900
AB - We introduce a new logarithmic digit variation for Vilenkin--Fourier partial sums and establish two-sided estimates for the corresponding Lebesgue constants with universal constants. These estimates hold for both bounded and unbounded Vilenkin systems. As an application, we show that bounded logarithmic variation yields uniform boundedness of the corresponding partial-sum operators on L_1, L_1-norm convergence for every integrable function, and almost everywhere convergence.
ER -