Geodesic
Order equalities in different metrics for moduli of smoothness of various orders
Ural mathematical journal, Tome 4 (2018) no. 2, pp. 24-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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IIn this paper, we obtain order equalities for the $k$th order $L_{q}(T)$-moduli of smoothness $\omega_{k}(f;\delta)_{q}$ in terms of expressions that contain the $l$th order $L_{p}(T)$-moduli of smoothness $\omega_{ l }(f;\delta)_{p}$ on the class of periodic functions $f\in L_{p}(T)$ with monotonically decreasing Fourier coefficients, where $1$ $k,l \in \mathbb{N},$ and $T=(-\pi,\pi].$
Keywords: Inequalities of different metrics for moduli of smoothness, Order equality, Trigonometric Fourier series with monotone coefficients. 
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     title = {Order equalities in different metrics for moduli of smoothness of various orders},
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Niyazi A. Il'yasov. Order equalities in different metrics for moduli of smoothness of various orders. Ural mathematical journal, Tome 4 (2018) no. 2, pp. 24-32. http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a3/

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