Some further results on belonging of trigonometric series to Orlicz space

Abstract

Here in this paper we have introduced a new condition which is not worse than thecondition that satisfy numerical sequences of Rest Bounded Variation Mean Sequences. This condition is used to obtain some integrability conditions of the functions g(x) and f(x) (which denote formal sine and cosine trigonometric series respectively) such that these functions aregoing to belong to the Orlicz space. This study may be considered as a continuation of theinvestigations previously done by L. Leindler [5] and S. Tikhonov [14].