Pointwise summability of Vilenkin--Fourier series

Abstract

In this paper we give a characterization of points in which Fejér means of Vilenkin-Fourier series converge.

Matrix transformations of sequences and applications in Fourier analysis

“…In [35] it is characterized the set of convergence of Vilenkin-Fejér means. It is introduced the following operator …”

Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions

“…Analogously, if use S 0 f = σ 0 f = 0, for any x ∈ G m and invoke Abel transformations (11) and ( 12) for b j = q j , a j = S j and A j = jσ j for any j = 0, 1, ..., n − 1 we get identities:…”

“…Moreover, in [11] (see also [10]) was proved that for any integrable function it is known that a.e. point is Vilenkin-Lebesgue points and for any such point x of integrable function f we have that…”

On the almost everywhere and norm convergences of Nörlund means with respect to Vilenkin systems

“…then the Féjer means of Fourier series of any integrable function converges a.e on G m to the function. Goginava and Gogoladze [27] introduced the operator W A defined by…”