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

N.T. Polovina

doi:10.15421/247719

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

N.T. Polovina (Dnipropetrovsk State University)

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.

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References

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