On a theorem of Stanojević
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- by William O. Bray PDF
- Proc. Amer. Math. Soc. 83 (1981), 59-62 Request permission
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.References
- John W. Garrett and Časlav V. Stanojević, On $L^{1}$ convergence of certain cosine sums, Bull. Amer. Math. Soc. 82 (1976), no. 1, 129–130. MR 394001, DOI 10.1090/S0002-9904-1976-13990-0 Č. V. Stanojević, Classes of ${L^1}$ convergence of Fourier and Fourier Stieltjes series, Proc. Amer. Math. Soc. (to appear).
- G. A. Fomin, A class of trigonometric series, Mat. Zametki 23 (1978), no. 2, 213–222 (Russian). MR 487218
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 59-62
- MSC: Primary 42A32; Secondary 42A20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0619981-4
- MathSciNet review: 619981