Remarks on the convergence (boundedness) in the mean of partial sums of a trigonometric series
This is a worthy paper with respectable results. The author gives fairly general conditions on the coefficients \(\{a_n\}\) of even and odd trigonometric Fourier series under which \(L\)-convergence (boundedness) of partial sums of the series is equivalent to the relation \[ \sum^{2n}_{k= [n/2]}|a_k|/(|n-k|+ 1)= o(1)\qquad (O(1),\text{ respectively}). \] {}.
scientific article; zbMATH DE number 1928219