Integrability and -convergence of Rees-Stanojević sums with generalized semiconvex coefficients.

Kaur, Kulwinder; Bhatia, S.S.

Displaying similar documents to “Integrability and $L^{1}$ -convergence of Rees-Stanojević sums with generalized semiconvex coefficients.”

On weighted $L^{p}$ integrability of functions defined by trigonometric series.

Szal, Bogdan (2010)

Journal of Inequalities and Applications [electronic only]

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Certain sums involving inverses of binomial coefficients and some integrals.

Yang, Jin-Hua, Zhao, Feng-Zhen (2007)

Journal of Integer Sequences [electronic only]

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On the behavior near the origin of double sine series with monotone coefficients

Xhevat Z. Krasniqi (2009)

Mathematica Bohemica

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In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients $a_{k, l}$ satisfy certain conditions) the following order equality is proved $g (x, y) \sim m n a_{m, n} + \frac{m}{n} \sum_{l = 1}^{n - 1} l a_{m, l} + \frac{n}{m} \sum_{k = 1}^{m - 1} k a_{k, n} + \frac{1}{m n} \sum_{l = 1}^{n - 1} \sum_{k = 1}^{m - 1} k l a_{k, l},$ where $x \in (\frac{π}{m + 1}, \frac{π}{m}]$ , $y \in (\frac{π}{n + 1}, \frac{π}{n}]$ , $m, n = 1, 2, \dots$ .