Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

Abstract

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.