In the spaces LΨ [0, 2𝜋] with the metric \( \rho \left(f,0\right)\varPsi =\frac{1}{2\pi }{\int}_0^{2\uppi}\varPsi \left(|f(x)|\right) dx \) , where is a function of Ψ the modulus-of-continuity type, we investigate an analog of the Nikol’skii–Stechkin inequalities for the increments and derivatives of trigonometric polynomials.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 5, pp. 711–716, May, 2017.
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Pichugov, S.A. Nikol’skii–Stechkin-Type Inequalities for the Increments of Trigonometric Polynomials in Metric Spaces . Ukr Math J 69, 831–837 (2017). https://doi.org/10.1007/s11253-017-1399-2
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DOI: https://doi.org/10.1007/s11253-017-1399-2