Absolute Nörlund summability of Fourier series of functions of bounded variation

On absolute Nörlund summability factors

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Local property of absolute weighted mean summability of Fourier series

We improve and generalize a result on a local property of |T |k summability of factored Fourier series due to Sarıgöl [6].

On the Convergence of Absolute Summability for Functions of Bounded Variation in Two Variables

and Applied Analysis 3 However, Wang and Yu 7 showed that Theorem A is not correct when 0 < α < 1. In fact, they proved the following. Theorem C. Suppose 0 < α < 1, x ∈ 0, π and f are 2π-periodic functions of bounded variation on −π,π . Then for n ≥ 2, one has Rn ( f, x ) ≤ 100 α2nα n ∑ k 1 kα−1Vπ/k 0 ( φx ) , 1.10 and there exists a 2π-periodic function f∗ of bounded variation on −π,π and a po...

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.