p. 243 - 252 On integrability conditions of functions related to the formal trigonometric
series belonging
to Orlicz space Xh. Z. Krasniqi Received: September 24, 2012;
Accepted: August 10, 2013
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
Keywords:
Trigonometric series; integrability; Orlicz space
AMS Subject classification:
Primary: 42A32, 46E30
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