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Ural Math. J., 2018, Volume 4, Issue 2, Pages 24–32 (Mi umj60)  

Order equalities in different metrics for moduli of smoothness of various orders

Niyazi A. Il'yasov

Baku State University, Baku, AZ 1148, Azerbaijan

Abstract: 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 $1<p<q<\infty,$ $k,l \in \mathbb{N},$ and $T=(-\pi,\pi].$

Keywords: Inequalities of different metrics for moduli of smoothness, Order equality, Trigonometric Fourier series with monotone coefficients.

DOI: https://doi.org/10.15826/umj.2018.2.004

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Citation: Niyazi A. Il'yasov, “Order equalities in different metrics for moduli of smoothness of various orders”, Ural Math. J., 4:2 (2018), 24–32

Citation in format AMSBIB
\Bibitem{Ily18}
\by Niyazi~A.~Il'yasov
\paper Order equalities in different metrics for moduli of smoothness of various orders
\jour Ural Math. J.
\yr 2018
\vol 4
\issue 2
\pages 24--32
\mathnet{http://mi.mathnet.ru/umj60}
\crossref{https://doi.org/10.15826/umj.2018.2.004}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR3901582}
\elib{http://elibrary.ru/item.asp?id=36702170}


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