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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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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: http://dx.doi.org/10.1090/S0002-9939-96-03212-1
PII: S 0002-9939(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