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.

References


Cook R. Infinite matrices and spaces of sequences, 1960. (in Russian)

Slepenchuk K.M. "Absolute summability in degree $$$p$$$ of Fourier series by triangular matrix methods", Res. Math., 1974; 5. (in Russian)

Polovina N.T "Absolute summability in degree $$$p$$$ of conjugate Fourier series by matrix methods", Res. Math., 1976. (in Russian)

Polovina N.T "Strong summability in degree $$$p$$$ of Fourier series by matrix methods", Res. Math., 1976. (in Russian)




DOI: https://doi.org/10.15421/247719

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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