On a local property of summability of Fourier series
We generalize and improve in some cases the results of Mahapatra and Chandra [7]. As a measure of Hölder norm approximation, generalized modulus-type functions are used.
Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.
Considering the class of almost periodic functions integrable in the Stepanov sense we extend and generalize certain results of the first author, as well as of L. Leindler and P. Chandra.
Recently, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - has proved some results on absolute Hausdorff summability of some series associated with Fourier series and its allied series, which generalise the results proved by Mohanty on absolute Cesaro summability. Proceeding on the similar lines, the author has generalised the results of Cheng - Duke Math. Jour., 15 (1948), 17-27 - by proving them on absolute Hausdorff summability.