Cesaro Summation of the Differentiated Series of Fourier-Lebesgue Series and their Allied Series

In this paper I discuss the summability of the differentiated series of Fourier-Lebesgue series and their allied series on lines similar to those adopted by Plessner‡, but remove the restriction that F(x) is to be a function of bounded variation. The general case of summability (C, k) for k > 0 for the differentiated series and k > 1 for the allied series is discussed, and known results are deduced as apecial cases.