On the strong $\left(L \right)$ summability of the derived Fourier series

Further result on the strong summability of Fourier series

This article deals with some special cases which are extension of the strong summability of Fourier series with constant factor. We obtain a new equivalent form of inequalities A 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) φ (z) 2 dρ r/2 dθ ≤ B 2π 0 φ(e iθ) r dθ, (1) 2π 0 1 0 (1 − ρ) q−1 φ (z) q dρ r/q dθ ≤ C 2π 0 φ(e iθ) r dθ, (2) D 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) p−1 φ (z) p dρ r/p dθ.

Almost Everywhere Strong Summability of Two-dimensional Walsh-fourier Series

A BMO-estimation of two-dimensional Walsh-Fourier series is proved from which an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series is derived.

Logarithmic Summability of Fourier Series

A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.

On the Summability of the Differentiated Fourier Series

Generalized matrix summability of a conjugate derived Fourier series

The study of infinite matrices is important in the theory of summability and in approximation. In particular, Toeplitz matrices or regular matrices and almost regular matrices have been very useful in this context. In this paper, we propose to use a more general matrix method to obtain necessary and sufficient conditions to sum the conjugate derived Fourier series.