Davit Baramidze, Zura Dvalashvili, Giorgi Tutberidze

Convergence of Nörlund Means with Respect to Vilenkin Systems of Integrable Functions

abstract:
In this paper, we derive the convergence of Nörlund means of Vilenkin-Fourier series with monotone coefficients of integrable functions at Lebesgue and Vilinkin-Lebesgue points. Moreover, we discuss pointwise convergence and convergence in $L_p$ norms of such Nörlund means.

Mathematics Subject Classification: 42C10, 42B25

Key words and phrases: Vilenkin systems, Vilenkin groups, Nörlund means, a.e. convergence, Lebesgue points, Vilenkin-Lebesgue points