Geodesic
A Fourier Formula for Series Summable (C, 1)
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 27-32

Voir la notice de l'article provenant de la source Cambridge University Press

Recently Bullen (1) developed a J 3-integral that gives a Fourier representation for trigonometric series when both the series and its conjugate are summable (C, 1) everywhere. Earlier Cross (4) had shown that the C 2P-integral (3) was strong enough to integrate such series and, indeed, that any trigonometric series for which the series and its conjugate were summable (C, k) were Fourier series where the integral used in the formula for the coefficients was the Ck+i P-integral (3). In (1) Bullen defines a J 4-integral and says, without proof, that a Fourier formula in terms of this integral may be obtained for series for which the series and its conjugate are summable (C, 2) and the coefficients o(n). 
Cross, George. A Fourier Formula for Series Summable (C, 1). Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 27-32. doi: 10.4153/CJM-1966-005-x
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[1] 1. Bullen, P. S., Construction of primitives of generalized derivatives with applications to trigonometric series, Can. J. Math., 13 (1961), 48–58. Google Scholar

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