Related papers: Logarithmic means of Walsh-Fourier Series

The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin-Fourier (Walsh-Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in…

In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.

The main objective of the present paper is to solve the several long standing divergence problems related to the logarithmic means of Fourier series in context of general orthonormal systems.

In this paper we investigate some convergence and divergence of some specific subsequences of partial sums with respect to Walsh system on the martingale Hardy spaces. By using these results we obtain relationship of the ratio of…

The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.

The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.

The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.

The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…

The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of…

We study de la Vall\'ee Poussin means of Walsh--Fourier series associated with a nondecreasing window sequence. We establish a sharp criterion for almost everywhere convergence for integrable functions. We further show that, when this…

We prove that, for functions in the Orlicz class LloglogLloglogloglogL, lacunary subsequences of the Fourier and the Walsh-Fourier series converge almost everywhere. Our integrability condition is less stringent than the homologous…

We prove that there exists a martingale $f\in H_p $ such that the subsequence $\{L_{2^n}f \}$ of N\"orlund logarithmic means with respect to the Walsh system are not bounded in the Lebesgue space $weak-L_p $ for $0<p<1 $. Moreover, we prove…

In this paper, we consider norm convergence for a special matrix-based de la Vall\'ee Poussin-like mean of Fourier series for the Walsh system. We estimate the difference between the named mean above and the corresponding function in norm,…

We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.e. Integral condition is only slightly larger than what the…

In the present paper, we give a brief review of $L^{1}$-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.

In this article, we present new generalizations of logarithmic convergence tests for number series, from which we will derive various new generalizations of the Jamet's convergence test. Further, similarly, on the basis of the…

The convergence of Ces\`{a}ro means of negative order of double trigonometric Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and neccessary conditions on the sequence $\Lambda…

In this paper we present results on convergence and Ces\`{a}ro summability of Multiple Fourier series of functions of bounded generalized variation.

In this paper we derive converge of $T$ means of Vilenkin-Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilinkin-Lebesgue points. Moreover, we discuss pointwise and norm convergence in $L_p$ norms of such…