On a necessary condition for $L^p$ $(0 < p < 1)$-convergence (upper boundedness) of trigonometric series | Zendy

Xh. Z. Krasniqi | Zendy

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On a necessary condition for $L^p$ $(0 < p < 1)$-convergence (upper boundedness) of trigonometric series

Author(s) -

Xh. Z. Krasniqi

Publication year - 2015

Publication title -

carpathian mathematical publications

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) , lambda , series (stratigraphy) , trigonometry , trigonometric functions , upper and lower bounds , trigonometric series , combinatorics , mathematical analysis , geometry , physics , quantum mechanics , paleontology , 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.

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