### 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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Szal, Bogdan (2010)

Journal of Inequalities and Applications [electronic only]

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

Journal of Integer Sequences [electronic only]

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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 $$g(x,y)\sim mn{a}_{m,n}+\frac{m}{n}\sum _{l=1}^{n-1}l{a}_{m,l}+\frac{n}{m}\sum _{k=1}^{m-1}k{a}_{k,n}+\frac{1}{mn}\sum _{l=1}^{n-1}\sum _{k=1}^{m-1}kl{a}_{k,l},$$ where $x\in (\frac{\pi}{m+1},\frac{\pi}{m}]$, $y\in (\frac{\pi}{n+1},\frac{\pi}{n}]$, $m,n=1,2,\cdots $.

Masjed-Jamei, Mohammad (2010)

Journal of Inequalities and Applications [electronic only]

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Grammel, G. (2007)

Abstract and Applied Analysis

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Sun, Zhiwei (2002)

Integers

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Krasniqi, Xhevat Z. (2011)

Applied Mathematics E-Notes [electronic only]

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Xhevat Z. Krasniqi (2013)

Archivum Mathematicum

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In this paper we introduce some new modified cosine sums and then using these sums we study ${L}^{1}$-convergence of trigonometric cosine series.

Dragan Dimitrovski, Vladimir Rajović (2007)

Kragujevac Journal of Mathematics

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