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  Volume 9, Issue 3, Article 69
On Integrability of Functions Defined by Trigonometric Series

    Authors: Laszlo Leindler,  
    Keywords: Sine and cosine series, $L^p$ integrability, equivalence of coefficient conditions, quasi power-monotone sequences.  
    Date Received: 15/01/08  
    Date Accepted: 19/08/08  
    Subject Codes:

26D15, 26A42, 40A05, 42A32.

    Editors: Sever S. Dragomir,  

The goal of the present paper is to generalize two theorems of R.P. Boas Jr. pertaining to $ L^p (p>1)$ integrability of Fourier series with nonnegative coefficients and weight $ x^gamma.$ In our improvement the weight $ x^gamma$ is replaced by a more general one, and the case $ p=1$ is also yielded. We also generalize an equivalence statement of Boas utilizing power-monotone sequences instead of $ {n^gamma}$.

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