Geodesic
Fourier Coefficients of Continuous Functions
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 691-703.

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It is well known that the Fourier coefficients of continuous functions with respect to classical orthogonal systems (trigonometric, Haar, and Walsh) can be estimated via the moduli of continuity of the functions. However, not all orthonormal systems possess this property. We obtain necessary and sufficient conditions on orthonormal systems such that the Fourier coefficients of continuous functions with respect to these orthonormal systems can be estimated via the moduli of continuity in a certain sense.
Keywords: orthonormal system, continuous function, modulus of continuity, Haar system, Hölder's inequality
Mots-clés : Fourier coefficients, Abel transform. 
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L. Gogoladze; V. Tsagareishvili. Fourier Coefficients of Continuous Functions. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 691-703. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a4/

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