Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 773997
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A55, 42A28

Retrieve articles in all journals with MSC: 42A55, 42A28


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0773997-X
PII: S 0002-9939(1985)0773997-X
Keywords: Lacunary Fourier series, absolute convergence, Lipschitz condition, bounded $ r$th variation
Article copyright: © Copyright 1985 American Mathematical Society