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

Acta Mathematica Academiae Paedagogicae Nyíregyháziensis

Xhevat Z. Krasniqi¹ 

[1] University of Prishtina

关键词: rest bounded second variation sequences.;   

DOI  :  

学科分类：数学（综合）

来源: Academia Paedagogica Nyiregyhaziensis. Acta Mathematica

【 摘 要 】

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.

【 授权许可】

Unknown