A note on the absolute convergence of lacunary Fourier series

Authors:
N. V. Patel and V. M. Shah

Journal:
Proc. Amer. Math. Soc. **93** (1985), 433-439

MSC:
Primary 42A55; Secondary 42A28

DOI:
https://doi.org/10.1090/S0002-9939-1985-0773997-X

MathSciNet review:
773997

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Abstract: P. B. Kennedy [**3**] studied lacunary Fourier series whose generating functions are of bounded variation on a subinterval of and satisfy a Lispschitz condition of order on . We show that the conclusion of one of his theorems on the absolute convergence of Fourier series remains valid when the function is merely of bounded th variation in and belongs to a class in . Our results also generalize three theorems of S. M. Mazhar [**4**].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0773997-X

Keywords:
Lacunary Fourier series,
absolute convergence,
Lipschitz condition,
bounded th variation

Article copyright:
© Copyright 1985
American Mathematical Society