Integrability of Double Cosine Trigonometric Series with coefficients of bounded variation of second order

• Autorzy: Krasniqi X. Z.
• Języki publikacji: EN

Abstrakty

EN

In this paper integrability condition for double cosine trigonometric series with coefficients of bounded variation of second order has been obtained. This condition is given explicitly in terms of the coefficients. The result extends a previous result of Telyakovskii from one dimensional case to two dimensional case

Słowa kluczowe

EN

trigonometric series; sequences of bounded variation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2011
• Tom: Vol. 51, [Z] 2
• Strony: 125--139
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Krasniqi X. Z.

• Department of Mathematics and Computer Sciences, University of Prishtina Avenue "Mother Theresa " 5, Prishtine 10000, Kosove,

Bibliografia

• [1] J. W. Garret, C. S. Rees and C. V. Stanojevic, L1 -convergence of Fourier series with coefficients of bounded variation, Proc. Amer. Math. Soc. 80 (3) (1980), 423-430.
• [2] S. B. Gembarskaya, Estimates for the variation of functions defined by double trigonometric cosine series, Ukrainian Math. Vol. 55, No. 6, (2003), 885-904.
• [3] A. N. Kolmogorov, Sur I'ordre de grandeur des coefficients de la sfrie de Fourier- Lebesgue, Bulletin de l'Academie Polonaise, 1923, 83-86.
• [4] Xh. Z. Krasniqi, Integrability of cosine trigonometric series with coefficients of bounded variation of order p, Appl. Math. E-Notes, 11 (2011), 61-66.
• [5] Xh. Z. Krasniqi, On the first derivative of the sums of trigonometric series with quasi-convex coefficients of higher order, Acta Comment. Univ. Tartu. Math., Vol. 14, 2010.
• [6] S. A. Telyakovskft, Localizing the conditions of integrability of trigonometric series (Russian), Theory of functions and differential equations, Collection of articles. To ninetieth birthday of Academician S. M. Nikolskii, Trudy Mat. Inst. Steklov., 210, Nauka, Moscow, 1995, 264-273. (Russian)