Open AccessOn a necessary condition for $L^p$ $(0 < p < 1)$-convergence (upper boundedness) of trigonometric series
Author(s) -
Xhevat Z. Krasniqi
Publication year - 2015
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.7.1.83-90
Subject(s) - mathematics , convergence (economics) , series (stratigraphy) , trigonometric series , lambda , trigonometry , trigonometric functions , upper and lower bounds , combinatorics , pure mathematics , mathematical analysis , geometry , physics , paleontology , optics , economics , biology , economic growth
In this paper we prove that the condition $\sum_{k=\left[\frac{n}{2}\right] }^{2n}\frac{\lambda _{k}(p)}{(|n-k|+1)^{2-p}}=o(1)\, \left(=O(1) \right),$ is a necessary condition for the $L^{p} (0<p<1)$-convergence (upper boundedness) of a trigonometric series. Precisely, the results extend some results of A. S. Belov.