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

 

On a theorem of Stanojević


Author: William O. Bray
Journal: Proc. Amer. Math. Soc. 83 (1981), 59-62
MSC: Primary 42A32; Secondary 42A20
MathSciNet review: 619981
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Abstract: A new direct proof of a theorem of Stanojević is given. Consequently it is proven that the Fomin class $ {\mathcal{F}_p}(1 < p \leqslant 2)$ is a subclass of the class $ \mathcal{B}\mathcal{V} \cap \mathcal{C}$, where $ \mathcal{C}$ is the Garrett-Stanojević class and $ \mathcal{B}\mathcal{V}$ is the class of null sequences of bounded variation. This also provides a new direct proof of Fomin's theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619981-4
PII: S 0002-9939(1981)0619981-4
Keywords: $ {L^1}$ convergence of Fourier series, integrability of cosine series
Article copyright: © Copyright 1981 American Mathematical Society