On the absolute convergence of Fourier series of the classes H^ω ∩ V [v]

Z. A. Chanturia

Vol. 96 (1981), No. 1, 37–61

DOI: 10.2140/pjm.1981.96.37

Abstract

In this paper the absolute convergence of the Fourier series is studied for the class of the function f with the modulus of continuity and the modulus of variation satifying the conditions ω(δ,f) = O(ω(δ)) and v(n,f) = O(v(n)) respectively, where the modulus of continuity ω(δ) and the modulus of variation v(n) are given. In terms of these properties the sufficient conditions of the absolute convergence are established. We prove that these conditions are unimprovable in certain sense.

Mathematical Subject Classification

Primary: 42A28

Milestones

Received: 2 November 1979

Published: 1 September 1981