Year: 2026
Type: preprint
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 \(L_1\), \(L_1\)-norm convergence for every integrable function, and almost everywhere convergence.
Source: arXiv (Cornell University)
Author: Tephnadze, George
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224123957