A note on the absolute convergence of lacunary Fourier series
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- by N. V. Patel and V. M. Shah PDF
- Proc. Amer. Math. Soc. 93 (1985), 433-439 Request permission
Abstract:
P. B. Kennedy [3] studied lacunary Fourier series whose generating functions are of bounded variation on a subinterval $I$ of $[ - \pi ,\pi ]$ and satisfy a Lispschitz condition of order $\alpha$ on $I$. 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 $r$th variation in $I$ and belongs to a class $\operatorname {Lip}(\alpha ,p)$ in $I$. Our results also generalize three theorems of S. M. Mazhar [4].References
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Additional Information
- © Copyright 1985 American Mathematical Society
- 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