Geodesic
Fourier Coefficients of Functions with a Given Modulus of Continuity
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 184-192

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In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.
Mots-clés : Fourier coefficient
Keywords: modulus of continuity of a function, system of Rademacher functions, $2\pi$-periodic function, convex function. 
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     author = {V. S. Biryukova},
     title = {Fourier {Coefficients} of {Functions} with a {Given} {Modulus} of {Continuity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {184--192},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/}
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V. S. Biryukova. Fourier Coefficients of Functions with a Given Modulus of Continuity. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 184-192. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a2/