Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods

The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence of Fejer means of Vilenkin–Fourier series was proved. In this paper, we present a different (and simpler) approach to prove a similar result, which can be used to prove that the corresponding result holds also in a more general context, namely for regular Norlund and T-means

Some weak type inequalities and almost everywhere convergence of Vilenkin–Nörlund means

Abstract We prove and discuss some new weak type ( 1 , 1 ) $(1,1 )$ inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out

Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods

The concept of Vilenkin-Lebesgue points was introduced in [12], where the almost everywhere convergence of Fejer means of Vilenkin-Fourier series was proved. In this paper, we present a different (and simpler) approach to prove a similar result, which can be used to prove that the corresponding result holds also in a more general context, namely for regular Norlund and T-means