$L^{1}$-convergence of Fourier series with coefficients of bounded variation
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- by J. W. Garrett, C. S. Rees and Č. V. Stanojević PDF
- Proc. Amer. Math. Soc. 80 (1980), 423-430 Request permission
Abstract:
It is shown that a Telyakovskii [2] theorem and its generalization are special cases of a corollary to a theorem of Garrett and Stanojević [4]. Another theorem of Garrett and Stanojević is generalized for the case of coefficients of bounded variation of order $m \geqslant 1$.References
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A. N. Kolmogorov, Sur l’ordre de grandeur des coefficients de la série de Fourier-Lebesgue, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. (1923), 83-86.
S. A. Telyakovskii, Concerning a sufficient condition of Sidon for the integrability of trigonometric series, Math. Notes 14 (1973), 742-748.
S. Sidon, Hinreichende Bedingungen fur den Fourier-charakter einer trigonometrischen Reihe, J. London Math. Soc. 14 (1939), 158-160.
J. W. Garrett and Č. V. Stanojević, Necessary and sufficient conditions for ${L^1}$ convergence of trigonometric series, Proc. Amer. Math. Soc. 80 (1976), 68-71.
- Charles S. Rees and Caslav V. Stanojevic, Necessary and sufficient conditions for integrability of certain cosine sums, J. Math. Anal. Appl. 43 (1973), 579–586. MR 322432, DOI 10.1016/0022-247X(73)90278-3 H. Mayer Marzuq, Necessary and sufficient conditions for integrability of certain cosine sums, Notices Amer. Math. Soc. 22 (1975), A-513.
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 423-430
- MSC: Primary 42A28
- DOI: https://doi.org/10.1090/S0002-9939-1980-0580997-7
- MathSciNet review: 580997