Abstract
First, it is proved that the class of classical quasi-monotone sequences is not comparable to the newly defined class of sequences of ‘rest bounded variation’. Considering this result, we prove three sample theorems for sequences of rest bounded variation, being analogues of the theorems proved earlier for monotone or quasi-monotone sequences. One of them gives a partial answer to a question raised by R. P. Boas Jr.
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R. ASKEY and S. WAINGER, Integrability theorems for Fourier series, Duke Math.J., 33(1966), 223–228.
R. P. BOAS, JR., Integrability of trigonometric series. III, Quart.J.Math.Oxford.Ser. (2), 3(1952), 217–221.
R. P. BOAS, JR., Integrability theorems for trigonometric transforms, Springer (Berlin–Heidelberg, 1967).
T. W. CHAUNDY and A. E. JOLLIFFE, The uniform convergence of a certain class of trigonometric series, Proc.London Math.Soc. (2), 15(1916), 214–216.
YUNG–MING CHEN, On the integrability of functions defined by trigonometrical series, Math.Z., 66(1956), 9–12.
YUNG–MING CHEN, Some asymptotic properties of Fourier constants and integrability theorems,, Math.Z., 68(1957), 227–244.
L. LEINDLER, On the uniform convergence and boundedness of a certain class of sine series, Analysis Math., 27(2001), 279–285.
S. M. SHAH, Trigonometric series with quasi–monotone coeficients, Proc.Amer.Math.Soc., 13(1962), 266–273.
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Leindler, L. A new class of numerical sequences and its applications to sine and cosine series. Analysis Mathematica 28, 279–286 (2002). https://doi.org/10.1023/A:1021717700626
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DOI: https://doi.org/10.1023/A:1021717700626