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The extensions of the Ferenc Móricz theorems


Authors: S. S. Bhatia and Babu Ram
Journal: Proc. Amer. Math. Soc. 124 (1996), 1821-1829
MSC (1991): Primary 42A16, 42A20
DOI: https://doi.org/10.1090/S0002-9939-96-03212-1
MathSciNet review: 1307497
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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.


References [Enhancements On Off] (What's this?)

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Additional Information

S. S. Bhatia
Affiliation: Department of Mathematics, Maharshi Dayanand University, Rohtak-124001, India

Babu Ram
Affiliation: Department of Mathematics, Maharshi Dayanand University, Rohtak-124001, India

DOI: https://doi.org/10.1090/S0002-9939-96-03212-1
Keywords: Modified complex trigonometric sums, weakly even sequences, $L^1$-convergence
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society

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