Geodesic
On sequences of Fourier coefficients of functions of Hölder classes
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 567-572 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following theorem is proved. Let $\{\psi_l(t)\}$ be an arbitrary complete orthonormal system on $[0,1]$ and let $1/2<\alpha<1$. Then an $f(t)\in C_\beta$ exists for all $\beta<\alpha$ such that $\sum_{k=1}^\infty|c_k(f)|^p=\infty$, $p=2/(1+2\alpha)$, where $c_k(f)=\int\limits_0^1f\psi_k\,dt$. 
@article{MZM_1969_6_5_a6,
     author = {G. S. Abros'kina and B. S. Mityagin},
     title = {On sequences of {Fourier} coefficients of functions of {H\"older} classes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {567--572},
     year = {1969},
     volume = {6},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a6/}
}
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G. S. Abros'kina; B. S. Mityagin. On sequences of Fourier coefficients of functions of Hölder classes. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 567-572. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a6/