The extension of the theorems of Č. V. Stanojević and V. B. Stanojević
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- by Shu Yun Sheng
- Proc. Amer. Math. Soc. 110 (1990), 895-904
- DOI: https://doi.org/10.1090/S0002-9939-1990-1031672-2
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Abstract:
The new necessary-sufficient conditions for ${L^1}$ convergence of Fourier series are obtained; Č. V. Stanojevic̀ and V. B. Stanojevic̀’s theorem [5] and Singh and Sharma’s theorem [2] are modified; the convergence theorem for a function sequence in ${L^1}$ space is obtained; and the extensions are made for the Sheng and Yang theorem [6] and Singh and Sharma’s results.References
- Niranjan Singh and K. M. Sharma, Convergence of certain cosine sums in a metric space — $L$, Proc. Amer. Math. Soc. 72 (1978), no. 1, 117–120. MR 503543, DOI 10.1090/S0002-9939-1978-0503543-3
- Niranjan Singh and K. M. Sharma, Convergence of a trigonometric series in the metric space $L$, Arabian J. Sci. Engrg. 4 (1979), no. 2, 137–140 (English, with Arabic summary). MR 554626
- Otto Szász, Quasi-monotone series, Amer. J. Math. 70 (1948), 203–206. MR 22917, DOI 10.2307/2371946 J. W. Garrett, C. S. Ress and Č. V. Stanojevic̀, Convergence of certain cosine sums in metric space- $L$, Proc. Amer. Math. Soc. 72 (1978), 534-537.
- Časlav V. Stanojević and Vera B. Stanojevic, Generalizations of the Sidon-Telyakovskiĭ theorem, Proc. Amer. Math. Soc. 101 (1987), no. 4, 679–684. MR 911032, DOI 10.1090/S0002-9939-1987-0911032-2
- Shu Yun Sheng and Yi Qun Yang, $L$-convergence of a class of trigonometric series, Acta Math. Sinica 28 (1985), no. 4, 503–508 (Chinese). MR 808034 S. A. Telyakovskii, On a sufficient condition of sidon for the integrability of trigonometric series, Math. Notes 14 (1973), 742-748.
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 895-904
- MSC: Primary 42A20; Secondary 42A32
- DOI: https://doi.org/10.1090/S0002-9939-1990-1031672-2
- MathSciNet review: 1031672