Geodesic
Estimates of the integral modulus of continuity of functions with
Sbornik. Mathematics, Tome 193 (2002) no. 9, pp. 1333-1347 Cet article a éte moissonné depuis la source Math-Net.Ru

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The functions under consideration are those satisfying the condition $\Delta a_i=\Delta b_i=0$ for all $i\ne n_j$, where $\{n_j\}$ is a lacunary sequence. An asymptotic estimate of the rate of decrease of the modulus of continuity in the $L$-metric of such functions in terms of their Fourier coefficients is obtained. 
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S. A. Telyakovskii. Estimates of the integral modulus of continuity of functions with. Sbornik. Mathematics, Tome 193 (2002) no. 9, pp. 1333-1347. http://geodesic.mathdoc.fr/item/SM_2002_193_9_a3/

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