Inequalities of Kolmogorov type for fractional derivatives of multivariable functions

V.F. Babenko (Oles Honchar Dnipropetrovsk National University, Institute of Applied Mathematics and Mechanics of NAS of Ukraine),
T.V. Matveeva (Oles Honchar Dnipropetrovsk National University)


We prove new sharp inequality of Kolmogorov type that estimates the norm of mixed fractional Marchaud derivative of n-variable function by C-norm of this function and its norms in Lipschitz spaces.


Samko S.G., Kilbas A.A., Marichev O.I. Integrals and derivatives of fractional order and their applications, Nauka i tekhnika, Minsk, 1987; 688 p. (in Russian)

Babenko V.F., Churilova M.S. "On inequalities of Kolmogorov type for derivatives of fractional order", Res. Math., 2001; 6: pp. 16-20. (in Russian)

Babenko V.F., Pichugov S.A. "Kolmogorov type inequalities for fractional derivatives of Holder functions of two variables", East J. Approx, 2007; 13(3): pp. 321-329.




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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991