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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |