V. F. Babenko, S. A. Pichugov, “Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying Hölder Conditions”, Mat. Zametki, 2010, Volume 87, Issue 1,Pages <nobr>26

This article is cited in 9 papers

Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying Hölder Conditions

V. F. Babenko^a, S. A. Pichugov^b

^a Dnepropetrovsk National University
^b Dnepropetrovsk National University of Railway Transport

Abstract: 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.

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

UDC: 517.5

Received: 05.06.2008
Revised: 26.05.2009

DOI: 10.4213/mzm5180