A note on the MRBSV S class and its application to the uniform convergence and boundedness of sine series

• Autorzy: Szal B.
• Języki publikacji: EN

Abstrakty

EN

A new class of γ rest bounded second variation sequences is dened. Some relationships between classes of considered sequences are proved. The results of Leindler [3] and author [8] are extended to our new class.

Słowa kluczowe

EN

sine series; Fourier series; embedding relations; number sequences

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2009
• Tom: Vol. 49, [Z] 1
• Strony: 67--79
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Szal B.

• University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics 65-516 Zielona Góra, ul. Szafrana 4a, Poland,

Bibliografia

• [1] T. W. Chaundy and A. E. Jolliffe, The uniform convergence of a certain class of trigonometrical series, Proc. London Math. Soc., 15(1916), 214-216.
• [2] R. J. Le and S. P. Zhou, A new condition for the uniform convergence of certain trigonometric series, Acta Math. Hungar., 108 (1-2) (2005), 161-169.
• [3] L Leindler, On the uniform convergence and boundedness of a certain class of sine series, Analysis Math., 27(2001), 279-285.
• [4] L. Leindler, A note on the uniform convergence and boundedness of a new class of sine series, Analysis Math., 31(2005), 269-275.
• [5] L. Leindler, Embedding results regarding to strong approximation of Fourier series VI, Acta Sci. Math. (Szeged), 71 (2005), 91-103.
• [6] L. Leindler, Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math., 8(2) (2007), Art. 38, 6 pp.
• [7] S. Tikhonov, Best approximation and moduli of smoothness: Computation and equivalence theorems, J. Approx. Theory, 153 (2008), 19-39.
• [8] B. Szal, A note on the uniform convergence and boundedness a generalized class of sine series, Commentat. Math., Comment. Math., 48 1(2008), 85-94.
• [9] D. S. Yu, S. P. Zhou and P. Zhou, Ultimate generalization to monotonicity for uniform convergence of trigonometric series, available at http://arXiv/abs/0704.1865.
• [10] A. Zygmund, Trigonometric series, Vol. I, University Press (Cambridge, 1959).