Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying H\"older Conditions

V. F. Babenko ; S. A. Pichugov

Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 26-34.

Résumé

We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on Hölder spaces.

Détail

Keywords: Marchaud fractional derivative, essentially bounded function, Kolmogorov-type inequality, Hölder condition, Hölder space.

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