Kolmogorov inequalities for norms of Marchaud-type fractional derivatives of multivariate functions

N.V. Parfinovych; V.V. Pylypenko

doi:10.15421/242007

Kolmogorov inequalities for norms of Marchaud-type fractional derivatives of multivariate functions

N.V. Parfinovych (Oles Honchar Dnipro National University)
V.V. Pylypenko (Oles Honchar Dnipro National University)

Abstract

We obtain new sharp Kolmogorov type inequalities, estimating the norm of mixed Marchaud type derivative of multivariate function through the C-norm of function itself and its norms in Hölder spaces.

Keywords

Kolmogorov inequality; fractional derivative; modulus of continuity; norm

MSC 2020

41A10; 41A17; 41A35; 41A65; 26A33; 26D10; 35A23; 41A29

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DOI: https://doi.org/10.15421/242007