A note on the absolute summability of Fourier series by Bosanquet-Linfoot method
The main result reads as follows. Let \(\Phi(t)=(f(x+t)+f(x-t))/2\) and \(\alpha\geq 0.\) If \(t^{-\alpha}\int_0^t(t-u)^{\alpha-1}\Phi(u) du\) is of bounded variation on \((0,\pi),\) then the Fourier series of an integrable \(2\pi\)-periodic function \(f\) is summable \(|\alpha,\beta|\) for all \(\beta\geq 1.\) In earlier results the range of \(\beta\) was narrower.
scientific article; zbMATH DE number 1848925