ORDER EQUALITIES IN DIFFERENT METRICS FOR MODULI OF SMOOTHNESS OF VARIOUS ORDERS

Niyazi A. Il'yasov     (Baku State University, Baku, AZ 1148, Azerbaijan)

Abstract


In 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 monotonic coefficients

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References


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DOI: http://dx.doi.org/10.15826/umj.2018.2.004

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