Vilenkin–Lebesgue points and summations of bounded multi-dimensional Vilenkin–Fourier series
Year: 2026
Type: article
Abstract: In 2017, Weisz introduced the concept of $$\omega $$ ω -Walsh–Lebesgue points and proved that the Fejér means $$\sigma _n (f)$$ σ n ( f ) of the Walsh–Fourier series of a d -dimensional integrable function f converge to the function at each $$\omega $$ ω -Walsh–Lebesgue point, provided that $$n \rightarrow \infty $$ n → ∞ and n lies within a cone. In this paper, we aim to generalize these results to the Vilenkin–Fejér means and other summability methods of Vilenkin–Fourier series. We also present convergence theorems for $$\theta $$ θ -summations as well as for matrix transform and Nörlund summations.
Source: Journal of Geometric Analysis
Authors: Máté Szilveszter, Rodolfo Toledo, Ferenc Weisz
Institution: Eötvös Loránd University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7204780746