Trigonometric approximation in generalized lebesgue spaces l-p(x)

Abstract

The approximation properties of Norlund (N-n) and Riesz (R-n) means of trigonometric Fourier series are investigated in generalized Lebesgue spaces L-p(x). The deviations parallel to f - N-n(f) parallel to(p(x)) and parallel to f - R-n(f) parallel to(p(x)) are estimated by n(-alpha) for f is an element of Lip(alpha, p(x)) (0 < alpha <= 1).