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 | References | Similar Articles | Additional Information
Abstract: We study the integrability of the 
times differentiated complex trigonometric series using modified trigonometric sums and obtain a new necessary and sufficient condition for 
-convergence of the 
th derivative of the Fourier series. Some results of F. Móricz are deduced as corollaries.
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-convergence, Trans. Amer. Math. Soc. 269 (1982), 677--683. 
-convergence of a modified cosine sum, Indian J. Pure Appl. Math. 19 (1988), 1101--1104. 
-convergence of complex trigonometric series, Proc. Amer. Math. Soc. 113 (1991), 53--64. Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42A16, 42A20
Retrieve articles in all journals with MSC (1991): 42A16, 42A20
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
