Geodesic
Some estimates of the rate of summability of orthogonal series by linear means
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 261-268

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An estimate of the rate of convergence of linear means of the orthogonal series of an $L^2$ function $f(x)$ generated by a summation function is established. This estimate depends on the rate of growth of factors which do not destroy the convergence of the series of squares of coefficients of $f(x)$ with respect to the orthonormal system under consideration. 
@article{MZM_1968_4_3_a1,
     author = {A. V. Efimov},
     title = {Some estimates of the rate of summability of orthogonal series by linear means},
     journal = {Matemati\v{c}eskie zametki},
     pages = {261--268},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a1/}
}
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A. V. Efimov. Some estimates of the rate of summability of orthogonal series by linear means. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 261-268. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a1/