Inequalities of Kolmogorov type for fractional derivatives of multivariable functions

V.F. Babenko; T.V. Matveeva

doi:10.15421/240801

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), https://orcid.org/0000-0001-6677-1914
T.V. Matveeva (Oles Honchar Dnipropetrovsk National University)

Abstract

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.

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References

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.