On integrability conditions of functions related to the formal trigonometric series belonging to Orlicz space

Abstract

In this paper we have introduced a new class of numerical sequences named as Mean Rest Bounded Variation Sequence of second order. This class is used to show some integrability conditions of the functions sin xg(x) and sin xf(x) such that these functions belong to the Orlicz space, where g(x) and f(x) denote formal sine and cosine trigonometric series, respectively. This study may be taken as an continuati on of some recent foregoing results proved by L. Leindler and S. Tikhonov