Geodesic
Fourier coefficients of functions of class $\mathrm{Lip}\,\alpha$ with respect to complete orthonormalized systems
Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 397-402.

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The Bernstein–Szasz theorem concerning trigonometric Fourier coefficients of a function of class $\mathrm{Lip}\,\alpha$ is generalized to apply to arbitrary complete orthonormalized systems. 
@article{MZM_1970_7_4_a3,
     author = {S. V. Bochkarev},
     title = {Fourier coefficients of functions of class $\mathrm{Lip}\,\alpha$ with respect to complete orthonormalized systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {397--402},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a3/}
}
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S. V. Bochkarev. Fourier coefficients of functions of class $\mathrm{Lip}\,\alpha$ with respect to complete orthonormalized systems. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 397-402. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a3/