Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 249-257 (2015)

Rest bounded second variation sequences and ${p}$-th power integrability of some functions related to sums of formal trigonometric series

Xhevat Z. Krasniqi

University of Prishtina

Abstract: In this paper we have studied ${p}$-th power integrability of functions $\sin xg(x)$ and $\sin xf(x)$ with a weight, where $g(x)$ and $f(x)$ denote the formal sum functions of sine and cosine trigonometric series respectively. This study may be taken as a continuation for some recent foregoings results proven by L. Leindler [Leindler, L. A new class of numerical sequences and its applications to sine and cosine series. Anal. Math. 28 (2002), no. 4, 279-286. MR1941748 (2003m:42010)] and S. Tikhonov [Tikhonov, S. Yu. On the integrability of trigonometric series. (Russian) Mat. Zametki 78 (2005), no. 3, 476-480; translation in Math. Notes 78 (2005), no. 3-4, 437-442 MR2227520 (2007a:42009)] employing the so-called rest bounded second variation sequences.

Keywords: Integrability of functions with a weight, trigonometric series, rest bounded second variation sequences.

Classification (MSC2000): 42A32; 46E30

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