We prove a new exact Kolmogorov-type inequality estimating the norm of a mixed fractional-order derivative (in Marchaud's sense) of a function of two variables via the norm of the function and the norms of its partial derivatives of the first order.
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Translated from Ukrains'kyi Matematchnyi Zhurnal, Vol. 60, No. 6, pp. 837–842, June, 2008.
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Babenko, V.F., Pichugov, S.A. On Kolmogorov-type inequalities for fractional derivatives of functions of two variables. Ukr Math J 60, 977–984 (2008). https://doi.org/10.1007/s11253-008-0099-3
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DOI: https://doi.org/10.1007/s11253-008-0099-3