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

Author(s): Xh. Z. Krasniqi

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 2;
Start page: 243;
Date: 2013;
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Keywords: Trigonometric series | integrability | Orlicz space

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 showsome 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 continuation of some recent foregoing results proved by L. Leindler and S. Tikhonov
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