On the utility of the Telyakovskii's class S

Volume 2, Issue 3, 2001

Article 32

ON THE UTILITY OF THE TELYAKOVSKII'S CLASS S

BOLYAI INSTITUTE, UNIVERSITY OF SZEGED,
ARADI VÉRTANÚK TERE 1,
6720 SZEGED, HUNGARY.
E-Mail: leindler@math.u-szeged.hu

Received 29 January, 2001; 26 April, 2001.
Communicated by: S.S. Dragomir

ABSTRACT. An illustration is given showing the advantage of the definition given by Telyakovski ${\u{\i\/}}\kern.15em$ for the class introduced by Sidon. It is also verified that if a sequence $\{a_n\}$ belongs to the recently defined subclass $S_\gamma$ of

, $\gamma >0$ , then the sequence $\{n^\gamma a_n\}$ belongs to the class

, but the converse statement does not hold.

Key words:
Cosine and Sine Series, Fourier Series, Fourier Coefficients, Inequalities, Integrability.

2000 Mathematics Subject Classification:
26D15, 42A20.

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