The extensions of the Ferenc Móricz theorems

Bhatia, S.; Ram, Babu

doi:10.1090/S0002-9939-96-03212-1

The extensions of the Ferenc Móricz theorems
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by S. S. Bhatia and Babu Ram

Proc. Amer. Math. Soc. 124 (1996), 1821-1829

DOI: https://doi.org/10.1090/S0002-9939-96-03212-1

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Abstract:

We study the integrability of the $r$ times differentiated complex trigonometric series using modified trigonometric sums and obtain a new necessary and sufficient condition for $L^1$-convergence of the $r$th derivative of the Fourier series. Some results of F. Móricz are deduced as corollaries.

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