We establish necessary and sufficient conditions for the validity of Bernstein-type inequalities for the fractional derivatives of trigonometric polynomials of several variables in spaces with integral metrics. The problem of sharpness of these inequalities is investigated.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 1, pp. 42–56, January, 2014.
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Kolomoitsev, Y.S. Inequalities for the Fractional Derivatives of Trigonometric Polynomials in Spaces with Integral Metrics. Ukr Math J 67, 45–61 (2015). https://doi.org/10.1007/s11253-015-1064-6
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DOI: https://doi.org/10.1007/s11253-015-1064-6