Geodesic
Order equalities in different metrics for moduli of smoothness of various orders
Ural mathematical journal, Tome 4 (2018) no. 2, pp. 24-32

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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. 
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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