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Convergence of a conjugate function in Zygmund space by almost Nörlund transform

Sharma Kusum, Dumka Diksha

Journal of Applied Analysis

2023

Vol. 29, nr 2

329--339

The proposed work aims to study the degree of convergence of a function ĥ, conjugate to a Lebesgue integrable 2π-periodic function h, in the Zygmund class Zr(ν), r ≥ 1, by almost Nörlund transform. Our results give sharper estimates than the previous existing results.

On approximation in generalized Zygmund class

Nigam Hare Krishna

Demonstratio Mathematica

2019

Vol. 52, nr 1

370--387

Here, we estimate the degree of approximation of a conjugate function ğ and a derived conjugate function ğ′, of a 2 π-periodic function g ∈ Zλr, r ≥ 1, using Hausdorff means of CFS (conjugate Fourier series) and CDFS (conjugate derived Fourier series) respectively. Our main theorems generalize four previously known results. Some important corollaries are also deduced from our main theorems. We also partially review the earlier work of the authors in respect of order of the Euler-Hausdorff product method.